NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Turbulence-Turbine Interaction: 

The Basis for the Development 

of the TurbSim Stochastic 

Simulator 

N.D. Kelley

Technical Report

NREL/TP-5000-52353

November 2011
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

National Renewable Energy Laboratory

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Golden, Colorado 80401

303-275-3000 • www.nrel.gov

Contract No. DE-AC36-08GO28308

Turbulence-Turbine Interaction: 

The Basis for the Development 

of the TurbSim Stochastic 

Simulator 

N.D. Kelley 

Prepared under Task No(s). WE11.0311

Technical Report

NREL/TP-5000-52353

November 2011
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Acknowledgments 

This work is currently supported by the U.S. Department of Energy (DOE) under contract no. 

DE-AC36-08GO28308. The author acknowledges the continued support of this research by the 

DOE Office of Wind and Hydropower Technologies and its predecessors from the embryonic 

stage of this research in 1989 through the present. The author specifically acknowledges Jack 

Cadogan for his continued support of this work over the years and more recently Mark Higgins 

for his patience in the production of this final report. 

The author particularly acknowledges Ed McKenna’s outstanding contributions to this research 

for more than 20 years. Without Ed’s unwavering personal loyalty and superior instrumentation, 

planning, and field operations expertise, we would never have been able to obtain the 

information that has been crucial in developing our understanding of how turbulence affects 

wind turbines. The support of David Jager and George Scott over the years is acknowledged and 

greatly appreciated. 

The author recognizes Bonnie Jonkman’s outstanding technical support of this work. Without 

Bonnie’s mathematical and programming skills, we would not been able to apply many of the 

sophisticated and state-of-the art analysis techniques that proved so useful. And the TurbSim 

turbulence simulator code would not be as comprehensive and useful as it is if it were not for her 

dedication and programming expertise. 

A very productive collaboration with Herbert Sutherland of Sandia National Laboratories helped 

put the impact of turbulence on the material properties of wind turbine structural components on 

a firm technical basis. 

Thanks go to Fort Felker of the National Wind Technology Center (NWTC) for his much 

appreciated and critical support. 

The author also thanks Yelena Pichugina of the University of Colorado and the National Oceanic 

and Atmospheric Administration and Pat Moriarty of the NWTC for their discussions and very 

valuable comments. 

iii 
 

Acronyms 

AGL	 above ground level 

ANOVA	 analysis of variance 

ART	 Advanced Research Turbine 

BM	 bending moment 

CART2, CART3	 Controls Advanced Research Turbine – Two 

Blades, Three Blades 

CoRA	 Colorado Research Associates 

CRR	 critical Richardson number stability range 

CRRH	 critical Richardson number stability range high 

CS	 coherent structure 

CTKE	 coherent turbulent kinetic energy 

CWT	 continuous wavelet transform 

DNS	 direct numerical simulation 

DOE	 U.S. Department of Energy 

DOF	 degrees of freedom 

DWT	 discrete wavelet transform 

ESRL	 Environmental Systems Research Laboratory 

(NOAA) 

ETM	 Extreme Turbulence Model (IEC) 

FIR	 finite impulse response 

GE Wind	 General Electric Wind Energy 

GP_LLJ	 TurbSim Great Plains Low-Level Jet Spectral 

Model 

GWI	 gravity wave instability 

HAWT	 horizontal axis wind turbine 

HRDL	 high-resolution Doppler lidar 

IEC	 International Electrotechnical Commission 

IECKAI	 TurbSim IEC Kaimal spectral model 

IECVKM	 TurbSim IEC von Kârmân spectral model 

IMU	 inertial measurement unit 

IQR	 Interquartile range 

K-H Kelvin-Helmholtz (other than KHI) 

KHI Kelvin-Helmholtz Instability 

KHTEST TurbSim severe turbulence option 

LES large-eddy simulation 

LIST Long-Term Inflow and Structural Test Program 

LLJ low-level jet stream 

LLLJP Lamar Low-Level Jet Project 

LOESS locally weighted regression 

LST local standard time 

ML mixed layer portion of PBL 

MLR multiple linear regression 

iv 
 

M-O	 Monin-Obukhov 

MSL	 mean sea level 

NACA	 National Advisory Committee for Aeronautics 

NASA	 National Aeronautics and Space 

Administration 

NCAR	 National Center for Atmospheric Research 

NOAA	 National Oceanic and Atmospheric 

Administration 

NREL National Renewable Energy Laboratory 

NTM	 Normal Turbulence Models as specified by the 

IEC (Kaimal, von Kârmân, or Mann) 

NWP	 Normal Wind Profile (IEC) 

National Wind Technology Center 

NWTCUP	 TurbSim NWTC spectral model 

PBL	 planetary boundary layer 

PDF	 probability density function 

RL	 residual layer portion of PBL 

PRTD	 platinum resistance temperature detector 

SGS	 subgrid scale 

SL	 surface layer portion of PBL 

SMOOTH	 TurbSim Rise homogeneous terrain spectral 

model 

SNL	 Sandia National Laboratories 

SNLWIND	 Paul Veers’ original turbulence simulation 

code 

SNLWIND-3D	 NREL update of SNLWIND inflow turbulence 

simulation code 

STC0x	 stability class where x = 1 to 5 

TKE	 turbulent kinetic energy 

UTC	 Coordinated Universal Time 

VAWT	 vertical axis wind turbine 

WF_xxx	 TurbSim wind farm spectral models: xxx = 

UPW, 07D, or 14D 

WindPACT	 Wind Partnership for Advanced Component 

Technologies 

WRF	 Weather Research and Forecasting Model 

v 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Nomenclature 

Atmospheric Variables 

mean shear stress profile, z o τ(z) τ() = ρ () z u w'  ' ( )z 



σu, σ1 streamwise or longitudinal wind component standard deviation 

σv crosswind or lateral wind speed component standard deviation 

σw vertical wind speed component standard deviation 

σT temperature standard deviation 

σ horizontal wind speed standard deviation UH 

τo surface shear stress 

θv virtual potential temperature (θ corrected for moisture) 

σw vertical wind speed standard deviation 

cp specific heat of air at constant pressure 

c perturbation phase speed 

cnU Chebyshev polynomial coefficients for low-level jet U-component 

cnθ Chebyshev polynomial coefficients for low-level jet wind direction 

Cohij Coherence function x 

ε turbulence viscous dissipation rate 

2 2 2 ET total turbulent kinetic energy (TKE), ET = 1/ 2( u′ + v′ + w′ )
 

Eiso isotropic turbulent kinetic energy, E iso T coh = E − E

Ecoh, CTKE coherent turbulent kinetic energy 

f reduced frequency, f = nz / U
 

g gravity acceleration
 

Ihub hub-height turbulence intensity, I hub U = σ /U H H 

IAT coherent turbulent structure event interarrival time
 

k wavenumber, k = 2 / π λ
 
 

κ von Kârmân constant (~0.4)
 

LM-O Monin-Obukhov length, u*

3 / L =− θ o kgQ 

Lb buoyancy length scale, Lb = σw / Nbuoy 

n cyclic frequency (Hz)
 

N or Nbuoy Brunt-Väisälä (buoyancy) frequency, Nbuoy = / θ)(∂θ ∂z) 2 (g / 

N(t) number of events in a Poisson counting process 

Ncoh number of coherent turbulent structures found in a 10-minute record 

p atmospheric pressure 

po reference atmospheric pressure (typically 1000 hectopascals (hPa, 

millibars [mb])
 

pkCTKE peak coherent turbulent kinetic energy, peak Ecoh
 

θ potential temperature, θ = T (1000 / p)

.286
 

α power law shear exponent, α = ln( U U/ ) / ln( z / z ) 2 1 2 1 

Qo surface heat flux
 

Ri gradient Richardson number, Ri θ ∂θ / ∂z U / ∂z)

2 = g / ( ) /( ∂
 

Ric critical Richardson number, Ri = +0.25
 

vi 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RiTL turbine layer gradient Richardson number stability parameter 

Rif flux Richardson number 

rij 

S(f) 

cross-correlation coefficient 

power spectral density 

STC stability class 

T sensible absolute temperature 

Tv virtual absolute temperature 

Tcoh total length of coherent turbulent structures in 10-minute record 

t time 

u streamwise wind component 

u* mean friction velocity or shearing stress, * u = uw ' '

u*D mean local u* value across rotor disk layer 

u’ streamwise eddy turbulence component 

UH Horizontal wind speed, UH = 2 2

u v +

U H mean U H

v crosswind or lateral wind component 

v’ crosswind or lateral eddy turbulence component 

w vertical wind component 

w’ vertical eddy turbulence component 

u w u v v w ' ', ' ', ' ' Reynolds stress components 

w’E vertical flux (transport) of turbulent kinetic energy (TKE) 

w’Ecoh vertical flux (transport) of coherent turbulent kinetic energy 

w’T’ buoyancy flux 

x coordinate in the direction of the mean wind 

y coordinate perpendicular to the mean wind in the horizontal plane 

z height coordinate 

zi mixed layer (ML) depth 

zo surface roughness length 

ρ air density 

λ wavelength, Poisson rate parameter 

z/L Monin-Obukhov stability parameter 

z/LD Mean z/L value across turbine disk layer 

ωx streamwise component of vorticity 

ωy crosswind or lateral component of vorticity 

ωz vertical component of vorticity 

H helicity, 1/ 2( ) H u = i i ω , where i = 1,2,3 

Turbine-Related Variables 

CT rotor thrust coefficient 

D turbine rotor diameter 

DEL damage equivalent load 

EBM blade root edgewise bending moment 

FBM blade root flapwise bending moment 

Mp-p alternating bending moment peak-to-peak loads or stress cycles 

vii 
 

 

 

Ncyc number of blade loading cycles 

β1 flapwise high-loading tail distribution exponential shape parameter 

γ 2 edgewise high-loading tail distribution extreme value shape parameter 

viii 
 

 

 

 

 

 

 

 

 

 

 

Executive Summary 

Introduction 

Analyses of the performance of the range of prototype wind turbines developed under the 

Federal Wind Program in the 1970s and early 1980s found that the structural fatigue damage 

sustained while operating in a wide range of environments far exceeded original design 

estimates. These excessive loads were attributed to the impact of atmospheric turbulence. More 

recently, with the return of turbine sizes and capacities at or exceeding those of the earlier 

multimegawatt prototypes, many of the same issues have resurfaced. Current designs do 

incorporate many of the lessons learned from the earlier generations. But they also tend to be 

more structurally flexible, and they are being installed and operated at greater heights above the 

ground. Even though the availability of today’s design tools has given the designers of the 

current generation of turbines a distinct advantage over their predecessors, the increased heights 

have introduced new challenges. As an example, turbines now operate deeper into the 

atmospheric boundary layer, where the turbulence characteristics can be significantly different 

from those closer to the ground. 

This combination of taller turbines with more flexible rotors and towers operating in turbulent 

conditions that are not as well understood is contributing to much higher than anticipated 

maintenance and repair costs and is associated with lower energy production. Statistical studies 

of wind farm productivity and operating costs with the currently installed fleet of turbines have 

shown a systemic power underproduction coupled with the need for more maintenance and 

repairs. Turbine availability has been estimated to account for almost half of this deficit, of 

which the downtime for repairs is a major constituent. The cumulative nature of the turbine 

lifetime trend in operating costs strongly suggests that the target operating environments for 

turbine design are somehow deficient (i.e., critical turbulent conditions are either being missed 

entirely or inadequately accommodated during design). In this report we document evidence of 

this and offer the turbine designer an expanded tool that resolves many of these shortcomings. 

Approach

In 1989, the Wind Technology Group at the National Renewable Energy Laboratory (NREL) 

began a program, sponsored by the U.S. Department of Energy (DOE), to develop a physical 

understanding of the role of atmospheric turbulence in the dynamic response of wind turbines. 

The program’s first objective was to develop a detailed understanding of the physics governing 

the interaction of atmospheric turbulence and the dynamic loading induced on turbine 

components. The next step was to quantify that interaction in terms of the dominant turbulence 

scaling parameters and their influence on the structural response and corresponding fatigue 

damage to wind turbine components. This is best accomplished by simultaneously measuring 

microscale characteristics (time and space scales of wind field motions smaller than the turbine 

rotor diameter); turbulence entering the rotor; and the dynamic loading response of key turbine 

components such as the blades, drivetrain, and tower. 

Between 1989 and 2000, two major field experiments were conducted to collect and analyze this 

type of information. We took measurements of operating turbines at a multirow wind farm in San 

Gorgonio, California (California wind farm) and at the National Wind Technology Center 

(NWTC) near Boulder, Colorado. In addition, we extended our knowledge of the factors 

controlling turbulence-induced response by looking at a planned wind farm at a high-altitude site 

ix 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

in the Great Plains, near Lamar in southeastern Colorado (the Lamar Low-Level Jet Project, or 

LLLJP). The greatest wind resource in the United States resides in the Great Plains and much of 

it (particularly during the warmer months) results from the presence of frequent nocturnal lowlevel jets (LLJs). 

To examine the synchronized time series of the turbine blade root loads and the three turbulence 

velocity components, we took measurements at the California wind farm and the NWTC with a 

hub-height upstream sonic anemometer or an array of sonic anemometers. 

Analyzing the field measurement campaigns gave us detailed insights into the turbulence 

characteristics that had the greatest impact on turbine dynamic loads and fatigue accumulation. 

Building on the groundbreaking work of Paul Veers of Sandia National Laboratories (SNL), we 

used this information to develop a stochastic turbulent inflow simulation (called TurbSim) that 

incorporates these critical flow characteristics. 

TurbSim runs simulations based on the International Electrotechnical Commission (IEC) Kaimal 

and von Kârmân Normal Turbulence Models (NTMs), as well as a spectral model for smooth, 

homogenous terrain developed at the Risø National Laboratory. In this report, however, we 

discuss the background and development of the site-specific spectral models representing 

turbulent conditions in and near the California wind farm, the NWTC, and the LLLJP site. These 

site-specific models are based on direct measurements taken at each location. 

With nocturnal LLJ streams and their strong vertical shears occurring frequently at the Great 

Plains site, including them in TurbSim was a primary objective of the measurement campaign 

there. To accomplish this, we made measurements of vertical profiles of wind speed and 

direction up to 500 m and collected data from a 120-m tower. A midrange acoustic wind profiler 

(sodar) was operated during the peak jet season to obtain characteristic jet profiles of wind speed 

and direction. Smoothed combined velocity and direction profiles derived from the tower and 

sodar were fitted with Chebyshev polynomials for a range of LLJ heights from 70 to 480 m in 

20-m increments. We arrived at a specific profile variation by scaling the Chebyshev coefficients 

with independent variables derived from the tower measurements. 

Report Objectives

In this report we discuss three major topics. First, we summarize our understanding of the role 

atmospheric turbulence plays in the dynamic response of wind turbines and the associated 

loading, along with its contribution to fatigue damage accumulation in key structural 

components. Next, we describe the atmospheric dynamics responsible for creating the turbulent 

conditions that can be the most detrimental to wind turbines. Finally, we briefly summarize the 

process in which the scaling was developed and incorporated into the turbulence spectral models 

that are available in TurbSim for the California wind farm, the NWTC, and the LLLJP. 

Results 

We summarize our results in three categories: the characterization of the turbine cyclic stress 

loading and its scaling relationships to inflow turbulence parameters; the atmospheric processes 

and conditions that influence these parameters; and the stochastic simulation of the turbulent 

inflow that incorporates critical flow structures. 

x 
 

 

 

 

 

 

 

 

 

 

Loading Characteristics and Their Relationships with Turbulence Scaling 

Parameters 

We found the following: 

•	 The probability of the most damaging blade root cyclic stresses was very highly 

correlated with the vertical dynamic stability of the atmospheric layer (expressed by the 

gradient Richardson number parameter Ri) measured from the ground to the top of the 

turbine rotor and the mean friction velocity or shearing stress (u*) within the layer 

occupied by the rotor. 

•	 The most damaging fatigue loads occur within the weakly stable range of +0.01 ≤ Ri < 

+0.05, with the maximum damage at a value of Ri = +0.02. The mean friction velocity u* 

also reached a maximum within this same stability range. 

•	 Similar correlations were found for two 65-kW turbines operating deep within the 41-row 

California wind farm and a 600-kW turbine operated at the NWTC, suggesting a 

universality of such correlations. 

•	 The sonic anemometer measurements revealed that the loads and the velocity 

components were associated with spatially and temporally organized or coherent 

turbulent structures or patches that were embedded in and moving with the basic or 

background wind flow. Such coherent structures occurred most frequently and were most 

intense within the stability range of +0.01 ≤ Ri < +0.05. This correlated well with our 

findings that the greatest fatigue damage takes place within the same range. The turbine 

loads scale very well with a parameter we define as coherent turbulent kinetic energy, or 

Ecoh. 

•	 Our initial attempt to simulate such turbine responses using a non-neutral expanded 

version of Veers’ original SNLWIND simulator called SNLWIND-3D, which included 

all three turbulent velocity components, was not completely successful. Although we 

were able to reproduce the body of the observed cyclic load distributions, the simulation 

did not include the few very large loads needed to match the observed fatigue damage. 

Atmospheric Processes That Influence Turbine Dynamic Loading

After we were unable to adequately reproduce the largest loading cycles in our simulation, we 

found that the simulation was not reproducing the most intense coherent turbulent structures seen 

in the natural flow. These structures, which were responsible for creating the largest cyclic loads, 

were missing in our inflow simulation even when the stability condition was specified within the 

critical Ri range discussed previously. The atmospheric instabilities that take place within this 

critical stability range offered a clue to the source of this discrepancy. We found the following: 

•	 Kelvin-Helmholtz Instability (KHI) taking place within and above the turbine rotor disk 

is ultimately responsible for the fewer but more damaging loads observed within the 

narrow stability range. 

•	 KHI transports energy from the mean background flow into intense coherent turbulent 

structures called billows that have a finite life span and grow and decay over a matter of 

minutes. 

xi 
 

 

 

 

 

 

 

 

 

 

•	 The fastest rate of billow formation and growth with the widest range of eddy sizes is 

initiated by a turbulent perturbation in the upstream flow. 

•	 A high-resolution computer simulation of the life cycle of a stationary Kelvin-Helmholtz 

(K-H) billow as the turbine inflow revealed that the largest turbine loads occur after the 

billow rolls over and begins to break down into smaller, coherent vortical structures. 

•	 Under these weakly stable conditions the limited buoyancy damping constrains the size 

of the largest eddy sizes in the coherent structure, which can be expressed as the 

buoyancy length scale, Lb. 

•	 The largest turbine loads generally occur when Lb is the same or slightly larger than the 

turbine rotor disk diameter. 

•	 Kinetic energy can be coherently transferred from the buoyancy-damped oscillating 

turbulent motions within coherent structures into the lightly damped modal frequencies of 

turbine blades and then into the remainder of the turbine structure. 

•	 Such organized spectral energy transfers or fluxes result in a phase-coherent summation 

of the amplitudes of the corresponding vibratory modes into a large load excursion. Put 

simply, a coherent turbulence excitation elicits a coherent aeroelastic response. 

•	 The KHI process is highly nonlinear and cannot be adequately reproduced using the 

Fourier inversion technique used in SNLWIND and SNLWIND-3D. 

Stochastic Simulation of Turbulent Inflows Containing Coherent Structures

Because the Fourier inversion technique used to replicate the velocity field in the TurbSim 

Program cannot be used to simulate the coherent structures, The structures generated by the KHI 

process had to be incorporated into the velocity time series of the background flow created by the 

Fourier inversion of the target turbulence frequency spectrum. This is more or less the way the 

process takes place in natural flows—the K-H billows are superimposed on the background flow 

while being fed from it. Eventually the strong vertical mixing created by the billow breakdown 

completely smears out any vestiges of the unstable perturbation into the background flow. 

To include coherent structures in TurbSim simulations, we 

•	 Extracted a number of self-contained excerpts of full 3-D, nondimensional coherent 

velocity structures from available high-resolution K-H billow computer simulations 

•	 Inserted versions of these structures into the TurbSim-simulated velocity time series that 

had been scaled based on the boundary conditions of the specific simulation 

•	 Chose total length and peak intensities of the structures randomly based on actual 

measurements at the California wind farm, at the NWTC, and at the LLLJP site; the 

characteristics of the coherent structures were scaled based on the specific boundary 

conditions of the simulation 

•	 Set the locations of coherent events within a record according to Poisson distribution 

based on the measured values of the event occurrence rate or interarrival time that was 

also scaled by the boundary conditions of the specific simulation. 

xii 
 

 

 

 

 

 

 

Conclusions 

In this report we present the following major conclusions: 

•	 When a turbine rotor ingests coherent structures or turbulent patches, generated large 

load excursions and fatigue damage often result. 

•	 Turbulent kinetic energy can be transported into the blade structure from these coherent 

structures that is then propagated through the root attachments into the drivetrain and the 

remaining structure where it is dissipated. 

•	 With the advent of increasingly taller towers and much larger and more flexible rotors, 

this vibratory energy flux process has most likely become more influential in creating 

fatigue damage throughout the turbine structure. 

•	 Coherent turbulent kinetic energy created locally within the rotor disk and externally 

transported into it is a major contributor to increased turbine fatigue damage. 

•	 KHI, which is associated with the stable atmospheric boundary layer, is most likely the 

dominant atmospheric process responsible for creating the coherent turbulent conditions. 

•	 There is a narrow but critical range of vertical dynamic stability where the largest 

damaging loads arise and typically occur within specific periods of the diurnal cycle. 

•	 The flows beneath Great Plains nocturnal LLJs contain coherent turbulent structures but 

often of a somewhat lesser intensity than those seen in the California wind farm and at 

the NWTC. The diurnal occurrence was similar to what we found in the wind farm and at 

the NWTC. Jets higher than the maximum height of turbine rotors were often responsible 

for significant downward fluxes (transport) of coherent turbulent energy similar to those 

seen in the lee flows downwind of mountain terrain. 

•	 The dearth of large loading events in turbine simulations using the TurbSim predecessor 

SNLWIND-3D was a result of the linear process of the Fourier inversion used to create 

velocity time series from specified frequency spectra. The most intense coherent 

structures result from the nonlinear KHI process. We solved this issue by inserting 

coherent structures, which had been generated by high-resolution numerical models that 

retained the nonlinearities, into the simulated background velocity fields. 

•	 We performed limited statistical validations of the stochastic wind field generated by the 

TurbSim code for the NWTC and LLLJP environments and found them to be in 

reasonable agreement. 

We believe that the TurbSim site-specific spectral models give the turbine designer realistic 

emulations of the true full-field turbulent inflows seen at each site, particularly within the 

critical stability range. As a result, we encourage turbine designers to use one of the available 

multibody dynamic codes with the NREL AeroDyn aerodynamics module as the interface to 

TurbSim simulations. 

xiii 
 

 

 

 

 

Contents 

Acknowledgments.......................................................................................................................... iii
 

Acronyms....................................................................................................................................... iv
 

Nomenclature................................................................................................................................. vi
 

Atmospheric Variables....................................................................................................... vi
 

Turbine-Related Variables................................................................................................ vii
 

Executive Summary....................................................................................................................... ix
 

Introduction........................................................................................................................ ix
 

Approach............................................................................................................................ ix
 

Report Objectives................................................................................................................ x
 

Results................................................................................................................................. x
 

Loading Characteristics and Their Relationships with Turbulence Scaling Parameters ... xi
 

Atmospheric Processes That Influence Turbine Dynamic Loading .................................. xi
 

Stochastic Simulation of Turbulent Inflows Containing Coherent Structures.................. xii
 

Conclusions...................................................................................................................... xiii
 

Contents ....................................................................................................................................... xiv
 

List of Figures............................................................................................................................. xvii
 

List of Tables ............................................................................................................................. xxxi
 

1.0 Introduction............................................................................................................................... 1
 

1.1 Inflow Turbulence and Turbine Response Research .................................................... 2
 

1.2 Field Measurements of Turbine-Turbulence Interactions............................................. 2
 

1.3 San Gorgonio Pass Wind Farm Experiment ................................................................. 3
 

1.3.1 The Turbines and Local Inflow Instrumentation ....................................................... 3
 

1.3.2 The Upwind and Downwind Met Towers ................................................................. 6
 

1.3.3 Synopsis of San Gorgonio Wind Characteristics....................................................... 7
 

1.4 NWTC Experiments...................................................................................................... 8
 

1.4.1 The ART .................................................................................................................... 8
 

1.4.2 A Synopsis of NWTC Wind Conditions.................................................................... 9
 

1.4.3 ART Upwind Planar Inflow Measurement Array.................................................... 12
 

1.5.1 LLLJP Measurements .............................................................................................. 13
 

2.0 Defining the Turbine Inflow Turbulence Characteristics ....................................................... 19
 

2.1 Wind Turbine Turbulence Operating Environment.................................................... 19
 

2.2 Turbulent Energy Production and Scaling.................................................................. 19
 

2.2.1 The TKE Budget...................................................................................................... 19
 

2.2.2 Atmospheric Stability .............................................................................................. 21
 

2.2.3 Identification of Turbulence-Turbine Response Scaling Variables......................... 23
 

3.0 Analyzing Turbulence-Turbine Dynamic Response of Micon 65/13 Turbines...................... 24
 

3.1 Identifying Turbine Response and Turbulence Scaling Parameters........................... 24
 

3.2 Measuring Fatigue Damage ........................................................................................ 31
 

3.3 Using Stochastic Turbulence Inflow Simulation ........................................................ 31
 

3.4 Further Quantifying Micon 65/13 Turbine Dynamic Response to Turbulence Scaling
 

Parameters......................................................................................................................... 32
 

3.5 Defining the Role of Coherent Turbulent Structures in Micon 65/13 Dynamic
 

Response ........................................................................................................................... 34
 

3.5.1 An Application of Wavelet Analysis ....................................................................... 35
 

xiv 
 

 

 

 

 

 

 

 

 

3.5.2 Defining a Variable That Represents the Level of Coherent Turbulent Energy in the
 

Flow .................................................................................................................................. 40
 

3.5.3 Statistical and Contour Analysis.............................................................................. 40
 

3.5.4 Expansion of Candidate Turbulence Parameter Predictors ..................................... 40
 

3.6 Identifying Micon 65/13 Turbulence Scaling Sensitivities ........................................ 44
 

3.6.1 Turbine Dynamic Response Sensitivity to Turbulent Velocity Characteristics ...... 44
 

3.6.2 Turbine Dynamic Response Sensitivity to Atmospheric Thermodynamics............ 50
 

3.7 Flow Details of Critical Stability Range..................................................................... 58
 

3.7.1 Role of Vertical Turbulence Transport .................................................................... 58
 

3.7.2 The Role of the Diurnal Variation and the Dynamics of the Critical Stability Range
 

........................................................................................................................................... 60
 

4.0 Analyzing Turbulence-Turbine Dynamic Response of the NWTC ART............................... 62
 

4.1 ART Dynamic Response to NWTC Inflow Turbulence Characteristics.................... 62
 

4.2 Vertical Inflow Inhomogeneity and Gradients within the ART Rotor Disk............... 66
 

4.3 NWTC ART Turbulence Scaling Sensitivities........................................................... 76
 

4.3.1 Turbine Aeroelastic Response to the NWTC Natural Inflow.................................. 76
 

4.4 ART Dynamic Response and Inflow Statistical Characteristics................................. 91
 

4.4.1 Relationship of ART Load and Turbulence Parameter Probability Distributions by
 

Stability Classification...................................................................................................... 93
 

4.4.1 Relationship of ART Load and Turbulence Parameter Probability Distributions by
 

Stability Classification...................................................................................................... 93
 

4.4.2 Diurnal Variations in NWTC Natural Inflow Characteristics and Observed ART
 

Load Extremes .................................................................................................................. 97
 

5.0 Comparing Micon 65/13 Turbines and ART Dynamic Responses in Their Turbulence
 

Operating Environments ............................................................................................................. 101
 

5.1 Comparing Full-Range Stability Classes.................................................................. 101
 

5.1.1 Turbine Dynamic Response Comparisons to Variations in Ecoh and σw ............... 101
 

5.1.2 Turbine Dynamic Response to Variations in Turbulence Scaling Characteristics 106
 

5.2 Comparing Hourly Diurnal Variations of Root FBM DEL Responses .................... 111
 

5.3 Defining Common Turbulence Characteristics ........................................................ 114
 

5.4 Comparing CRR Turbine Response Scaling Parameters.......................................... 114
 

5.5 Comparing Probability Distributions of Micon 65/13 Turbines and ART Root FBM
 

Responses by Stability Class .......................................................................................... 117
 

6.0 Atmospheric Dynamics Associated with Turbine Response ................................................ 122
 

6.1 Comparing Turbine Responses by Stability Class.................................................... 122
 

6.2 Defining Role of Turbulent Buoyancy in Turbine Dynamic Response.................... 128
 

6.2.1 Relationship between Shear and Buoyancy Turbulence Generation..................... 128
 

6.2.2 Buoyancy Damping and Length Scale................................................................... 128
 

6.2.3 Effects of Turbulent Buoyancy Damping on Characteristics of Turbine Dynamic
 

Response ......................................................................................................................... 133
 

6.3 Atmospheric Dynamics Associated with CRR Stability Range ............................... 138
 

6.3.1 Dynamics of KHI................................................................................................... 139
 

7.0 Coherent Turbulent Structures and Turbine Response ......................................................... 145
 

7.1 Kelvin-Helmholtz Billow Numerical Simulation ..................................................... 145
 

7.2 Turbine Dynamic Response to a Simulated K-H Billow.......................................... 152
 

7.3 Flux of Coherent Turbulent Energy into Turbine Structures.................................... 163
 

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7.4 Propagation of Coherent Turbulent Energy into Turbine Structure ......................... 170
 

7.5 Extension to Larger Turbine Rotors ......................................................................... 171
 

7.6 Modeling Coherent Turbulent Structures ................................................................. 178
 

7.7 Measured Turbine Dynamic Response to Observed Coherent Structures................ 179
 

7.8 Observed Coherent Structure Characteristics ........................................................... 189
 

8.0 Supporting the Extension of Larger Turbine Rotors to Higher Elevations in the Great Plains
 

Operating Environment............................................................................................................... 197
 

8.1 Interpreting LLLJP Results....................................................................................... 197
 

8.1.1 Analyzing the Lamar Measurement Database ....................................................... 198
 

8.2 Role of the Great Plains LLJ in Coherent Turbulence Generation and Transport
 

within the Rotor Disk...................................................................................................... 207
 

8.2.1 Case Studies for June 17, 2002.............................................................................. 207
 

8.2.2 Lidar Measurements of LLJ-Induced Turbine Layer Coherent Turbulence.......... 213
 

8.2.3 Low-Level Jet Statistical Characteristics............................................................... 217
 

8.2.4 LLJs and Turbulent Coherent Structures ............................................................... 222
 

9.0 TurbSim Scaling—A Brief Overview .................................................................................. 226
 

9.1 Background............................................................................................................... 226
 

9.2 Important Parameters and Conditions To Be Simulated........................................... 227
 

9.3 TurbSim Independent Scaling Variables .................................................................. 230
 

9.4 Developing Turbulence Scaling for NREL Site-Specific Spectral Models from Field
 

Measurements ................................................................................................................. 231
 

9.4.1 General Analysis and Modeling Procedure ........................................................... 231
 

9.4.2 Modeling the Turbulent Spectral Energy Distributions......................................... 235
 

9.4.3 Cross-Component Correlation and Mean Reynolds Stress Component Scaling... 251
 

9.4.4 Spatial Coherence Scaling ..................................................................................... 258
 

9.4.5 Coherent Structure Scaling and Implementation ................................................... 264
 

9.4.6 Lamar Site LLJ Wind Speed and Direction Profile Scaling.................................. 273
 

9.4.7 TurbSim Spatial Simulations ................................................................................. 283
 

9.5 Validation of TurbSim NWTCUP and GP_LLJ Spectral Models............................ 288
 

10.0 Summary and Conclusions ................................................................................................. 292
 

10.1 The Impact of Turbulence on Turbine Dynamics................................................... 292
 

10.2 Atmospheric Dynamics Associated with Turbine Dynamic Response .................. 293
 

10.3 Simulating Critical Turbulence Characteristics...................................................... 294
 

11.0 Bibliography ....................................................................................................................... 295
 

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List of Figures 

Figure 1-1. Row 37 of California wind farm: (a) looking downwind at the two test turbines 

(AeroStar rotor-equipped on the left, NREL rotor-equipped on the right) with the upstream met 

tower; (b) looking upstream (westward) from Row 37 at sunset; (c) looking north with NREL 

data trailer at Row 38...................................................................................................................... 4 

Figure 1-2. California wind farm Micon 65/13 turbine power curves........................................... 5 

Figure 1-3. Terrain characteristics surrounding California wind farm. The approximate shape of 

the farm is shown with the locations of the upwind and downwind 50-m met towers and the two 

test turbines at Row 37.................................................................................................................... 6 

Figure 1-4. Diurnal variation of hourly percentiles of hub-height mean wind speed U H 

(distributions from test of Micon 65/13 turbines at Row 37 of wind farm in 1990. The rated wind 

speed for the Micon 65/13 turbine with the NREL rotor is shown as a horizontal dashed line. 

Local sunrise (sr) and sunset (ss) for mid-July 1990 are shown as vertical dash-dot-dotted lines. 

The strongest winds typically occurred around 2200 local standard time (LST)........................... 7 

Figure 1-5. NWTC, location of the ART, and approximate position of upwind planar array of 

five sonic anemometers and other meteorological instrumentation ............................................... 9 

Figure 1-6. Topography upwind of NWTC. The inset shows the topography cross section along 

the prevailing wind direction (dashed line). ................................................................................. 10 

Figure 1-7. East-west vertical cross section through Boulder, Colorado, from 20-km resolution 

Weather Research and Forecasting (WRF) model operational prediction for 1500 GMT on 

January 13, 2011. The arrows parallel the wind flow and their length is proportional to the speed. 

The solid lines indicate the potential temperature. The shaded areas represent relative humidity, 

with the highest values in darkest green. The approximate position of the NWTC is shown. A 

moderate downslope wind event is forecast with warmer and drier air being brought down by the 

indicated winds. ............................................................................................................................ 10 

Figure 1-8. Observed NWTC box-plot probability distributions of 80-m (a) turbulence intensity, 

I80, and (b) U-component standard deviation, σ1 or σu ................................................................ 11 

Figure 1-9. Upwind planar measurement array used for measuring turbulent inflow to NWTC 

ART. The maximum and minimum heights were 58 and 15 m, with the left, center, and lateral 

measurements at the hub height of 37 m and spaced 21 m apart. The array was located 65 m 

upwind of the turbine rotor plane.................................................................................................. 12 

Figure 1-10. Location of LLLJP experiment site and 120-m tower in high plains of southeastern 

Colorado: (a) regional topography and (b) local topography ....................................................... 15 

Figure 1-11. Enron (GE) Wind 120-m met tower, southeastern Colorado (LLLJP site) ............. 16 

Figure 1-12. Close-up of NREL turbulence-measuring instrumentation installed on Enron (GE) 

120-m LLLJP tower...................................................................................................................... 16 

Figure 1-13. Instrumentation layout at LLLJP measurement site: (a) tower; (b) nearby sodar; (c) 

Scintec MFAS sodar antenna within enclosure; and (d) plan view of site layout ........................ 17 

Figure 1-14. NOAA/ESRL HRDL lidar in operation at LLLJP site: (a) position of lidar with 

respect to 120-m tower; (b) NOAA’s Robert Banta making observations; (c) vertical scans 

through evolving LLJ. The strongest winds in the last frame on the lower right would be at the 

top of the GE 1.5-MW turbine rotors now installed at this site. Wind speed scale is at the top, 

with negative values indicating the wind was coming toward the lidar. Times are in UTC 

(18:24:30 to 18:51:17 MST). ........................................................................................................ 18
 

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Figure 3-1. Schematic of relationship of high-frequency, low-amplitude Gaussian stress cycle 

distributions with lower frequency, high-amplitude exponentially distributed stress cycles ....... 25 

Figure 3-2. Schematic showing definition of exponential fit to high-amplitude, low-frequency 

tail of alternating stress cycle distribution .................................................................................... 25 

Figure 3-3. Example of root flapwise root bending spectrum from AWT-26 turbine installed in 

Tehachapi Pass, California............................................................................................................ 26 

Figure 3-4. Examples of two aggregated record periods of 111.5 and 19.3 hours of root edgewise 

cyclic load spectra from modified Micon 65/13 “M” turbine installed in Bushland, Texas, for 

mean wind speeds in 11- to 13-m s–1 range. The peak near 20 kNm is the cyclic load induced by 

gravity. .......................................................................................................................................... 27 

Figure 3-5. Variation of blade root load (a) flapwise (β1) and (b) edgewise (γ 2) shape parameters 

with hub-height u* and RiTL ......................................................................................................... 30 

Figure 3-6. Comparison of measured and simulated Micon 65/13 turbine with NREL rotor root 

flapwise load distributions at Row 37 in California wind farm.................................................... 32 

Figure 3-7. Significant loads seen on Micon 65/13 NREL and AeroStar rotors: (a) load 

excursions in flapwise and edgewise root loads; (b) corresponding instantaneous u’v’ and v’w’ 

Reynolds stresses and estimated local vorticity components ωy and ωz. H is the local relative 

helicity, a measure of the intensity of the spin in the structure. A coherent turbulent structure 

exists in the flow between about 3 and 6.5 seconds to which the turbine rotors responded......... 36 

Figure 3-8. Continuous wavelet decomposition of inflow turbulence Reynolds stress components 

and root flapwise bending load of NREL-rotor-equipped Micon 65/13 turbine .......................... 37 

Figure 3-9. Continuous and discrete wavelet decomposition of Micon 65/13 turbine blade root 

flapwise bending response to SNLWIND-3D simulated inflow containing embedded coherent 

structure. The uppermost panel is the time series of the hub-height wind speed, the second panel 

contains the time series of the three Reynolds stress components, the third panel is the flapwise 

bending load with the mean removed, the fourth panel is the continuous wavelet transform 

decomposition of the flapwise bending load, and the bottom panel is the discrete transform 

decomposition into seven frequency bands, with B7 the lowest frequency (0.125–0.25 Hz) and 

B1 the highest (8–16 Hz). ............................................................................................................. 38 

Figure 3-10. Continuous wavelet decompositions (scalograms) of simulated individual Reynolds 

stress components of coherent turbulent structure and corresponding response of Micon 65/13 

turbine root flapwise bending load ............................................................................................... 39 

Figure 3-11. Variation of NREL-rotor-equipped Micon 65/13 three-blade peak root FBM DEL 

with (a) hub peak Ecoh only and (b) RiTL and hub peak Ecoh. Negative values of RiTL indicate 

dynamically unstable, zero neutral, and positive stable flow conditions...................................... 42 

Figure 3-12. Variation of blade root FBM DELs for NREL and AeroStar rotors with hub-height 

mean wind speed for all available records.................................................................................... 45 

Figure 3-13. Comparison of variation of (a) three-blade averaged FBM DEL and (b) slope (β1) of 

high-loading tail with RiTL. The dashed lines in (a) delineate a critical or sensitive stability range 

for loads with the dot-dot-dashed line representing the most sensitive Ri value.......................... 46 

Figure 3-14. LOESS-smoothed contours of variation of FBM DELs from NREL-rotor-equipped 

Micon 65/13 turbine with RiTL and hub-height local u* value. Dashed and dot-dot-dashed lines 

correspond to those of Figure 3-13a delineating a critical stability range for loads..................... 47 

Figure 3-15. Variation of FBM loads: (a) three-blade average DELs vs. RiTL and hub u*; (b) 

three-blade average DELs vs. RiTL and hub peak Ecoh; (c) largest FBM value vs. RiTL and hub 

u*; (d) largest FBM value vs. RiTL and hub peak Ecoh ................................................................. 48 

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Figure 3-16. Variation of three-blade averaged FBM DELs with RiTL and standard deviations of
 

hub-height turbulence components σu , σv , and σw ...................................................................... 49
 

Figure 3-17. Variation of three-blade averaged FBM DELs with RiTL and ratios of σv /σu, σw /σu, 

and σw /σv . The dashed line of 0.8 on the σv/σu plots indicates the scaling used in the IEC Kaimal 

Figure 3-17. Variation of three-blade averaged FBM DELs with RiTL and ratios of σv /σu, σw /σu, 

and σw /σv . The dashed line of 0.8 on the σv/σu plots indicates the scaling used in the IEC Kaimal 

Figure 3-19. Variation of hub-height mean horizontal wind speed with RiTL. The critical RiTL
 

Figure 3-20. Variation of peak FBM loads with RiTL, hub-height turbulence intensity, Ihub, and 

Figure 3-21. Variation of Micon 65/13 turbine with NREL rotor three-blade average FBM DEL
 

with hub-height (a) σT and (b) buoyancy flux, ' ' ................................................................... 54
 

NTM.............................................................................................................................................. 49
 

NTM.............................................................................................................................................. 49
 

Figure 3-18. Variation of peak FBM loads with RiTL and hub-height mean Reynolds stresses .. 51
 

range is shown between +0.01 and +0.05 (dashed lines).............................................................. 52
 

peak Ecoh ....................................................................................................................................... 53
 

w T 
 

Figure 3-22. Variation of peak FBM loads with stability and mean buoyancy flux .................... 55
 

Figure 3-23. Variation of peak low-speed shaft bending loads with RiTL and the hub-height vw ' '

Reynolds stress component........................................................................................................... 55
 

Figure 3-24. Variation of peak low-speed shaft bending loads with stability and hub u* and Ecoh
 

Figure 3-25. Variation of nacelle axial thrust force (kN) on Micon 65/13 turbine equipped with 

....................................................................................................................................................... 56
 

NREL rotor with hub-height u* and peak Ecoh ............................................................................. 57
 

Figure 3-26. Details of variation of fluxes in critical stability range: (a) w T' ' and uw ' '; (b) 

positive and negative w E' coh values; and (c) σ Ecoh ......................................................................... 59
 

Figure 3-27. Observed diurnal variations of Uhub, RiTL, hub u* and peak Ecoh, negative peak
 

w’Ecoh, and three-blade average FBM DELs for Micon 65/13 NREL and AeroStar rotors. Each 

data point represents the values from an individual 10-minute record......................................... 61
 

Figure 4-1. Variations of NWTC ART root bending moment DEL with hub-height (a) peak Ecoh
 

Figure 4-2. Variations of FBM with hub-height peak Ecoh: (1) DELs, (2) maximum alternating
 

(rainflow) cycle, (3) peak value, and (4) peak value with mean removed for entire available 

Figure 4-4. Confirmation that hub peak Ecoh (CTKE) values greater than 10 m2 s

–2 are indicative 

and (b) mean wind speed .............................................................................................................. 63
 

population (left column) and below-rated wind speed (right column) ......................................... 64
 

Figure 4-3. Same as Figure 4-2, except with variation with hub-height mean wind speed.......... 65
 

– of significant response and resulting DEL: (a) probability distribution of FBM DEL with 10 m2 s
 1 threshold shown; (b) box plots of FBM DEL distributions for values of peak Ecoh ≤10 and > 10 

m2 s

–2 ............................................................................................................................................. 67
 

Figure 4-5 (a) Available population of expected variation of ART rotor disk shear exponent α
	

with hub (37-m) mean wind speed for unstable (RiTL < 0) and stable (RiTL > 0) flows; (b) 

variation of FBM DEL with rotor disk α. In general, the FBM DELs are not well correlated with
 

Figure 4-6. Variation of (a) rotor disk shear exponent α and (b) hub-height mean wind speed with 

α, although the lowest values tend to occur at its highest values.................................................. 68
 

RiTL. The critical RiTL value range of +0.01 to +0.05 found in the California wind farm is also 

shown. The mean wind speeds drop significantly above an RiTL value of +0.1. ......................... 69
 

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Figure 4-7. Variation of (a) hub-height peak Ecoh, (b) FBM DELs, and (c) hub-height σw with 

RiTL. The critical RiTL stability range found in the California wind farm (+0.01 to +0.05) is 

shown as dashed lines. .................................................................................................................. 70 

Figure 4-8. Observed variation of hub friction velocity u* with (a) RiTL and (b) hub mean wind 

speed. Critical RiTL stability range is shown as red dashed lines in (a) and the ART rated wind 

speed is a black dashed line in (b). The variations of the FBM DELs with hub-height u* are 

plotted in (c).................................................................................................................................. 71 

Figure 4-9. Correlation of blade FBM DELs with height variation of standard deviations of (a) 

vertical wind component σw and (b) vertical flux of coherent turbulent kinetic energy, w’Ecoh.. 72 

Figure 4-10. (a) Correlation of blade FBM DELs with height variation of peak values of vertical 

flux of coherent turbulent kinetic energy, w’Ecoh; (b) variation of peak value of w’Ecoh at the top 

of the ART rotor (58 m) with RiTL. The California wind farm critical stability range is shown 

between the vertical dashed lines.................................................................................................. 74 

Figure 4-11. Relationship of blade root flapwise DELs with height variations in peak Ecoh and 

mean vertical momentum flux, u w' ' ............................................................................................. 75 

Figure 4-12. Smoothed variations of NWTC ART mean root flapwise (left) and edgewise (right) 

bending moments with RiTL and (a) hub-height U ; (b) disk averaged u* ; and (c) hub-height 

peak Ecoh . The dashed line in (a) represents the rated wind speed, 12.8 m s–1. The vertical white 

dashed line indicates the upper limit of the critical stability range............................................... 77 

Figure 4-13. Smoothed variations of NWTC ART IMU forward nacelle accelerations with RiTL 

and mean disk-averaged turbulent Reynolds stress components u w' ', u v ' ' , and v w' ' . The 

variation of the fore-aft acceleration ( X ) is shown in the left column, the side-to-side or lateral 

acceleration (Y) in the center column, and the vertical acceleration ( Z) in the right column...... 78 

Figure 4-14. Smoothed variations of NWTC ART IMU forward nacelle X, Y, and Z acceleration 

responses (mg or g/1000) with RiTL and disk-averaged buoyancy flux wT ' ' in the top row, peak 

Ecoh in the center row, and Ecoh vertical flux, w E' in the bottom row ...................................... 79 coh 

Figure 4-15. Smoothed variations of NWTC ART IMU forward nacelle X, Y, and Z mean 

acceleration responses (mg) with RiTL and disk-averaged standard deviations of u-component ( 

σ u ) in top row, v-component ( σ v ) in center row, and w-component ( σ w ) in bottom row .......... 80 

Figure 4-16. Smoothed variations of NWTC ART nacelle IMU peak longitudinal (±X) [columns 

(a) and (b)] and positive vertical (+Z) [column (c)] peak acceleration responses (g) with RiTL and 

hub height: U (top row); peak Ecoh (center row); and local shear stress or friction velocity u* 

(bottom row) ................................................................................................................................. 81 

Figure 4-17. Smoothed variations of NWTC ART nacelle IMU peak angular response rates 

(positive in column [a] and negative in column b) with RiTL and hub-height mean wind speed U 

with pitch angle response (top row), roll angle response (center row), and yaw angle response 

(bottom row). Horizontal dashed line indicates rated wind speed................................................ 83 

Figure 4-18. Smoothed variations of NWTC ART nacelle IMU peak angular response rates 

(positive in column [a] and negative in column [b]) with RiTL and hub-height peak Ecoh with 

pitch angle response (top row), roll angle response (center row), and yaw angle response (bottom 

row)............................................................................................................................................... 84 

Figure 4-19. Smoothed variations of NWTC ART low-speed shaft torque standard deviation στ

(kNm) with RiTL and disk-averaged mean Reynolds stresses uw ' ', u v ' ' , and vw ' ' in upper row 

and standard deviations of streamwise (u), lateral (v), and vertical (w) turbulent wind 

components in lower row .......................................................................................................... 85 

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Figure 4-20. Smoothed NWTC ART variation of root FBM DEL with RiTL and disk-averaged (a) 

local friction velocity u* and (b) peak Ecoh. Upper limit of critical stability range is shown with 

vertical dashed line. ...................................................................................................................... 86 

Figure 4-21. Smoothed NWTC ART variation of root FBM DEL with RiTL and hub-height 

turbulence intensity (Ihub) ............................................................................................................. 87 

Figure 4-22. Smoothed variation of NWTC ART largest flapwise bending load with RiTL and 

disk-averaged local shearing stress or friction velocity u* ........................................................... 88 

Figure 4-23. Smoothed variations of NWTC ART FBM DELs with disk-averaged (a) uw ' ', (b) 

u v' ' , (c) vw ' ' , and (d) wT ' ' ............................................................................................................ 89 

Figure 4-24. Smoothed variations with height of NWTC ART FBM DELs with RiTL and (a) 

uw ' ' , (b) uv ' ', (c) vw ' ', and (d) wT ' ' ...................................................................................... 90 

Figure 4-25. Available NWTC ART response and inflow turbulence data by stability class...... 92 

Figure 4-26. Probability distributions of both ART dynamic response and range of inflow 

turbulence parameters by stability class. Turbine response variables: (a) root FBM DELs, (b) 

largest FBM load cycle, and (c) peak FBM load. Inflow parameters: (d) hub mean U, (e) diskaverage local u*, (f) rotor layer Rif, (g) rotor disk peak Ecoh, (h) rotor disk-average w E' coh , and (i) 

rotor disk layer shear exponent α.................................................................................................. 94 

Figure 4-27. Probability distributions of 58-m height peak Reynolds stress components (a) u w' ', 

(b) u v' ' , and (c) v w' ' . Note the much greater values associated with the u v' ' component, 

particularly for the CRR stability class, and significant decreases for the more stable CRRH and 

much more stable STC04 classes. Also note the separations in the mean and medians for the 

STC02 and CRR stability classes that indicate the presence of strong, heterogeneous (nonGaussian) conditions..................................................................................................................... 95 

Figure 4-28. Probability distributions by stability class of (a) peak buoyancy flux ( wT ' ' ) at top 

of ART rotor (58 m) and (b) mean buoyancy fluxes at top and bottom of turbine rotor (15 m) 

where dots represent P05 and P95 quantiles................................................................................. 96 

Figure 4-29. Boxplot presentation of probability in diurnal variation in NWTC 50-m mean wind 

speed observed during LIST observational period from October 1999 to May 2000. The 

horizontal dashed line represents rated wind speed for the ART. The cut-in wind speed was about 

6 m s–1. .......................................................................................................................................... 98 

Figure 4-30. Boxplot presentation of probability distributions of diurnal variation of RiTL when 

ART was operating during LIST experiment ............................................................................... 98 

Figure 4-31. Diurnal variations in (a) P90 and P95 quantiles of ART root FBM DEL distributions 

and (b) corresponding total number of hours of available observations for each time hour period. 

The few observations from 2100 to 2400 hours are the consequence of wind conditions that were 

often too severe for turbine operation........................................................................................... 99 

Figure 4-32. Diurnal variation in quantiles of (a) RiTL during ART operation and (b) 

corresponding P90 and P95 quantiles of probability distributions of observed root FBM DELs. 

The low values in (b) between 2200 and 2400 LST are a consequence of the turbine frequently 

not operating because of severe wind conditions. ...................................................................... 100 

Figure 5-1. Observed variations of root FBM DELs with RiTL for (a) Micon 65/13 turbines in 

Row 37 of California wind farm and (b) NWTC ART operating in natural inflow at Row 4. The 

CRR stability range is identified by the vertical dashed lines and the value of peak Micon turbine 

response (+0.02) is shown as a vertical dot-dot-dashed line. ..................................................... 102 

Figure 5-2. Comparisons of variations of hub-height peak Ecoh, root FBM DELs, and hub σw 

with RiTL observed at (a) Micon 65/13 turbines at Row 37 of California wind farm and (b) ART 

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on Row 4 of NWTC. The RiTL associated with maximum Micon turbine response (+0.02), the 

upper limit of the CRR range (+0.05), and the nominal upper limit of observed significant Micon 

dynamic responses (+0.10) are shown as dot-dot-dashed, dashed, and dotted vertical lines, 

respectively. ................................................................................................................................ 103 

Figure 5-3. Comparison of vertical fluxes of peak coherent turbulent kinetic energy (w′Ecoh) 

inflows to (a) hub height of Micon 65/13 turbine rotors at Row 37 in California wind farm; and 

(b) at the bottom (15 m), hub (37 m), and top (58 m) of NWTC ART rotor on Row 4 . The 

downward fluxes are shown in the left column and the upward in the right column. The CRR 

stability range is shown between the dashed vertical lines......................................................... 104 

Figure 5-4. Observed variations of root FBM DELs with mean and peak values of vertical flux of 

Ecoh (w’Ecoh) for (a,b) hubs of the California wind farm Micon 65/13 turbines and (d,e) 15-, 37­

(hub), and 58-m heights of the NWTC ART rotor disk. Variations of the maximum values of 

w’Ecoh with the mean value for the wind farm turbines are shown in (c) and for the ART in (f). 

..................................................................................................................................................... 105 

Figure 5-5. Observed variations of root FBM DELs with hub-height turbulence intensity (Ihub) 

and local friction velocity u* for the (a) Micon 65/13 turbines and (b) ART............................. 107 

Figure 5-6. Observed variations of rotor disk shear exponents (α) and hub-height mean 

horizontal wind speed UH of (a) Micon 65/13s and (b) ART root FBM DELs ......................... 108 

Figure 5-7. Comparison of variation of rotor disk shear exponents with RiTL for (a) Micon 

turbines and (b) ART .................................................................................................................. 110 

Figure 5-8. Observed variations of hub u* values with RiTL and hub mean horizontal wind speed 

(UH ) for (a) Row 37 of wind farm and (b) upwind of ART. The vertical red dashed lines shown 

in the upper row of graphs correspond to the value of RiTL (+0.02) in which the maximum 

dynamic response of the Micon turbines was observed.............................................................. 112 

Figure 5-9. Comparison diurnal variations of root FBM DEL responses for (e) Micon 65/13 

turbines and (f) ART with (a,b) uw ' ' and σw, (c,d) RiTL and buoyancy flux ( wT ' ' ). Nominal 

sunrise and sunsets are indicated by solid blue vertical lines. The critical stability values ranges 

(RiTL = +0.02, +0.05, and +0.10) are shown as horizontal lines in (c,d). Disk-averaged values of 

σw, uw ' ' , and wT ' ' are used for the ART variables.................................................................. 113 

Figure 5-10. Diurnal hourly probability of occurrence of CRR stability class conditions as seen 

for Micon 65/13 turbines on Row 37 of California wind farm and for ART on Row 4 at NWTC 

..................................................................................................................................................... 115 

Figure 5-11. Observed hub-height mean U-component wind speeds probability distributions in 

the CRR stability range for the Micon 65/13 turbines and for ART. Each has been fitted with a 

Gaussian distribution, shown as solid lines. The rated wind speeds for the Micon 65/13 turbine 

equipped with the NREL rotor and the ART are shown as vertical dashed lines....................... 116 

Figure 5-12. Variation of thrust coefficient CT with mean wind speed for Micon 65/13 turbine 

with NREL rotor. Highest probable mean U wind speed in data set shown as vertical dot-dotdashed line. (CT data source: J. Tangler, NREL) ....................................................................... 116 

Figure 5-13. Observed hub-height shearing stress or u* probability distributions in CRR stability 

range for the Micon 65/13 turbines and ART. Each has been fitted with a Gaussian distribution 

shown as solid lines. ................................................................................................................... 119 

Figure 5-14. Observed hub-height shearing peak Ecoh probability distributions in CRR stability 

range for Micon 65/13 turbines and ART. Each has been fitted with a Gaussian distribution, 

shown as solid lines. ................................................................................................................... 119 

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Figure 5-15. Observed hub-height fluxes of w’Ecoh for CRR stability range at Row 37 of the 

wind farm and Row 4 of the NWTC: (a) means and (b) peak values. Each has been fitted with a 

Gaussian distribution, shown as solid lines. ............................................................................... 120 

Figure 5-16. Comparison of Micon 65/13 turbine and ART cumulative probability distributions 

of root FBM DELs and peak loads for available populations [] and stability classes STC02 [∆], 

CRR [], CRRH [  ], and STC04 [] . Micon 65/13 with NREL rotor FBM: (a) three-blade 

averaged DELs; (b) three-blade peak. Micon 65/13 with AeroStar rotor FBM: (c) three-blade 

averaged DELs; (d) three-blade peak. NWTC ART FBM: (e) DELs; (f) peaks......................... 121 

Figure 6-1. Boxplot probability distributions of observed root FBM DELs and peak load 

responses by stability class for California wind farm Micon 65/13 (NREL rotor) turbine and 

NWTC ART. The dots represent values outside the P10–P90 range indicated by the whiskers. 

..................................................................................................................................................... 123 

Figure 6-2. Probability distributions of observed inflow hub-height mean U-component, rotor 

disk shear exponent and hub mean vertical buoyancy flux by stability class for Micon 65/13 

(NREL rotor) turbine and the ART. The dashed lines indicate the rated wind speeds. The boxplot 

nomenclature is the same as for Figure 6-1. ............................................................................... 124 

Figure 6-3. Probability distributions of inflow hub-height peak Ecoh vertical fluxes (w′Ecoh) for 

Micon 65/13 (NREL rotor) turbine and ART. The boxplot nomenclature is the same as for Figure 

6-1. .............................................................................................................................................. 126 

Figure 6-4. Comparison of probability distributions of Micon 65/13 (NREL rotor) turbine and 

ART hub peak Ecoh (upper panels) and blade root FBM DELs (lower panels) by stability class. 

Dashed line in upper panels (peak Ecoh) represents the significant turbine dynamic response 

threshold. The boxplot nomenclature is the same as for Figure 6-1........................................... 127 

Figure 6-5. Variation of measured mean buoyancy flux ( wT ' ') with RiTL and mean vertical 

momentum flux ( ' ' or u*

2 uw ) with height for natural inflow into ART. The red vertical dashed 

lines outline the CRR stability range, the dot-dot-dash line identifies the California turbines 

maximum response, and the dotted line indicates the upper limit of the CRRH stability range.130 

Figure 6.6. Probability distributions of Lb/D ratio by stability class for (a) Micon 65/13 turbine 

(NREL rotor) and (b) ART. The Lb for the Micon 65/13 turbine is based on the hub-height ơw 

and the disk-averaged ơw for the ART........................................................................................ 131 

Figure 6-7. Correlation of Lb/D ratios and FBM DELs with RiTL for Micon 65/13 turbines and 

ART. A trend line has been fitted to each of the distributions. .................................................. 132 

Figure 6-8. Example of effects of weakly stable flow buoyancy damping on loads seen on Micon 

65/13 turbine with NREL rotor. Polar plots looking downwind of the rotor azimuth of FBM 

loads instantaneously measured on each blade........................................................................... 134 

Figure 6-9. Summary of major inflow turbulence parameters influencing ART peak root FBM (a) 

peak cyclic stresses in stable flow; (b) RiTL; (c) intensity of coherent turbulent structures given 

by hub-level peak Ecoh (CTKE); and (d) buoyancy length scale Lb /D with stability ranges shown 

..................................................................................................................................................... 136 

Figure 6-10. Schematic example of consequences on turbine FBM loads from stable turbine layer 

buoyancy damping using both Micon 65/13 turbines and ART................................................. 137 

Figure 6-11. Schematic representation of vertical profiles of mean wind speed U(z) and 

temperature T(z) across turbine rotor disk layer D in stably stratified shear inflow. These profiles 

represent the background or reference flow conditions on which perturbations evolve linearly 

from this equilibrium state.......................................................................................................... 140 

Figure 6-12. Growth rate of fastest growing K-H mode as function of shear layer Ri............... 141 

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Figure 6-13. K-H mode growth rates and wavenumber (wavelength) range for three values of
 

shear layer Ri............................................................................................................................... 142
 

Figure 6-14. Example of K-H mode growth rates as function of shear layer depth in ART rotor
 

diameters and Ri over that layer. Observed Micon turbines and ART CRR stability class is
 

indicated with dashed lines, upper limit of CRRH class as the dotted line , and maximum 

Figure 6-7. Same as Figure 6-7, repeated for ease of comparison. There is a strong correlation 

between the region of fastest growing K-H modes shown above in the CRR range and the Lb /D
 

Figure 7-1(a). Maximum K-H billow 2-D structure at about t = 30 seconds, with secondary
 

Figure 7-1(c). Fully mixed flow (saturated) by t ≈ 170 seconds, with internal waves forming at 

Figure 7-2. Cloud formation of evolving K-H billows. Flow and evolution are from right to left.
 

Figure 7-3. Time series of evolving stationary K-H billow at y = 30 and z = 85 m. The phases of
 

Figure 7-4. Evolution of K-H billow used as input to simulation of WindPACT 1.5-MW baseline 

Figure 7-5. Time histories of hub-height UH, u’, v’, and w’, u’w’, u’ v’, and v’w’ and ET and Ecoh
 

Figure 7-6. Time histories of hub-height UH, and fluxes of momentum (shear stress) u’w’, ET, 

and Ecoh for two periods. Period (a) is characterized by the intense downward fluxes of
 

momentum, total (ET), and coherent (Ecoh) turbulent kinetic energy as the K-H billow rolls over
 

and breaks into fully 3-D motions. Period (b) is characterized by much smaller scale turbulent
 

Figure 7-7. Decrease in rotor layer mean vertical shear during life cycle of simulated K-H billow
 

Figure 7-8. Wavelet analysis of dynamic response of WindPACT baseline turbine zero-mean
 

root bending moment to simulated stationary K-H billow: (a) scalogram of decomposition by
 

continuous wavelet transform—deep reds indicate high dynamic stress levels and dark blue low
 

levels; (b) decomposition of root load time series with discrete wavelet transform. Bandwidths of
 

the discrete wavelet transform frequency bands D4 through D9 are shown in Table 7-2. High 

Figure 7-9. Continuous and discrete wavelet decompositions of root flapwise bending load 

induced in WindPACT turbine model from LES K-H billow simulation. The time history of the
 

blade root flapwise bending load with the mean removed is plotted in the second panel from the
 

Figure 7-10. Spectral flux of coherent turbulent energy from NCAR LES simulated K-H billow
 

Figure 7-11. Relative spectral energy flux (coscalogram) of Ecoh to blade dynamic pressure (qc )
 

at 78% span for simulated inflows of (a) IEC Kaimal NTM; (b) stable flow with high shear
 

dynamic response with the dot-dot-dashed line.......................................................................... 144
 

and root FBM fatigue damage on both the Micon turbines and the ART. ................................. 144
 

instabilities by t = 44 seconds and strong turbulence formation afterward ................................ 147
 

Figure 7-1(b). Fully 3-D turbulent flow by t = 70 seconds......................................................... 148
 

upper and lower boundaries........................................................................................................ 149
 

..................................................................................................................................................... 150
 

the evolution—formation, turbulent breakdown, and fully mixed saturation—are indicated.... 151
 

turbine ......................................................................................................................................... 153
 

input into WindPACT baseline turbine model............................................................................ 154
 

motions containing both positive and negative fluxes................................................................ 155
 

..................................................................................................................................................... 156
 

frequency response in the root load time series is highlighted by the red oval. ......................... 157
 

top. The dot-dashed vertical lines mark coherent responses across a frequency range of 1.875 to 

30 Hz as a result of the blade marked with the dashes encountering the coherent structures in the
 

center top panel........................................................................................................................... 162
 

into WindPACT rotor blade at 78% blade span station.............................................................. 164
 

(SMOOTH spectral model); and (c) breaking NCAR LES K-H billow..................................... 167
 

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Figure 7-12. Relative energy flux coscalogram between Ecoh and qc at simulated WindPACT 

turbine 78% span station for inflow from IEC Kaimal NTM spectral model simulation........... 168 

Figure 7-13. Relative energy flux coscalogram between Ecoh and qc at simulated WindPACT 

turbine 78% span station for inflow from high shear SMOOTH model simulation. Lowamplitude energy flux indicated with dashed lines is associated with frequencies greater than 10 

Hz................................................................................................................................................ 168 

Figure 7-14. Relative energy flux coscalogram between Ecoh and qc at simulated WindPACT 

turbine 78% span station for inflow from NCAR LES K-H billow simulation. Significant energy 

flux indicated with dashed lines is associated with frequencies greater than 10 Hz. ................. 169 

Figure 7-15. Relative energy flux coscalogram between Ecoh and qc at simulated WindPACT 

turbine 78% span station for inflow from CoRA DNS K-H billow simulation. Significant energy 

flux indicated with dashed lines is associated with frequencies greater than 10 Hz. ................. 169 

Figure 7-16. Coherent turbulence induced severe transient loading event measured on NWTC 

ART during LIST Project by blade zero-mean root loads and nacelle velocities measured on 

forward low-speed shaft support bearing.................................................................................... 174 

Figure 7-17. Observed energy propagation caused by coherent turbulent event excitation between 

low-speed shaft torque and (a) out-of-plane and (b) in-plane root bending loads and nacelle 

velocities measured on forward low-speed shaft support bearing immediately behind rotor .... 175 

Figure 7-18. Correlation of Micon 65/13 FBM DELs and peak values with RiTL from records in 

which peak Ecoh exceeded 5 m2 s

–2. The pair of vertical dashed lines represents the range of the 

CRR stability class, the dot-dot-dashed line the RiTL value (+0.02) of maximum response, and 

the dotted line the upper limit of the CRRH stability class (+0.05 ≤RiTL < +0.10). The 

moderately stable STC04 class extends from this dotted line to the limit of the diagram (RiTL = 

+0.25).......................................................................................................................................... 181 

Figure 7-19. Observed variations of Micon 65/13 FBM DELs and peak values with total length 

of coherent structures (Tcoh) in a 10-minute record. The vertical dot-dashed line indicates the 

median Tcoh value associated with records with the NREL rotor FBM DEL > P90. The red solid 

and dashed trend lines represent LOESS smoothing with a 0.5 overlap. ................................... 183 

Figure 7-20. Observed variations of the Micon 65/13 FBM DELs and peak values with number 

of coherent structures (Ncoh) in a 10-minute record. The vertical dot-dashed line indicates the 

median Ncoh value associated with records with the NREL rotor FBM DEL > P90. ................. 184 

Figure 7-21. Observed variations of Micon 65/13 FBM DELs and peak values with intensity 

(peak Ecoh) found in coherent structures within a 10-minute record. The vertical dot-dashed line 

indicates the median peak Ecoh associated with records with the NREL rotor FBM DEL > P90. 

..................................................................................................................................................... 185 

Figure 7-22. Variation of Lb/D ratio for Micon 65/13 (NREL rotor) with RiTL. The black vertical 

lines indicate the P25-P50-P75 range of the RiTL associated with the high loading tail (FBM DEL 

> P90). The stability classes and the max response RiTL = +0.02 are also as red vertical lines. 

Note that at the median RiTL value of +0.016 in Table 7-6, the Lb /D ratio for the NREL rotor is 1 

or the buoyancy length scale is equivalent to the rotor diameter. This indicates that the fastest 

growing K-H mode is the same scale as the rotor diameter and a source of the high fatigue loads. 

..................................................................................................................................................... 187 

Figure 7-23. Observed variation of intensity of the coherent structures (peak Ecoh) within a 10­

minute record as a function of buoyancy length scale Lb normalized by Micon 65/13 NREL rotor 

diameter. The median of the peak Ecoh (16.80 m2 s

–2) in Table 7-6 for the high loading tail shown 

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by the dot-dot-dashed horizontal line. This value intersects with the LOESS-smoothed trend line
 

at a Lb /D ratio of 1 as highlighted by the circle......................................................................... 189
 

Figure 7-24. California wind farm, NWTC, and Lamar probability distributions of measured 

coherent structure characteristics with 10-minute records: intensity (peak Ecoh), total length
 

Figure 7-25. California wind farm, NWTC, and Lamar probability distributions of local U, 

friction velocity u*, and vertical velocity standard deviation σw corresponding to measured 

Figure 7-27. Variations of coherent structures IAT with local U velocity and RiTL for upwind of
 

Rows 1 and 37 and downwind of Row 41 in California wind farm; at 15-, 37-, and 58-m heights
 

at NWTC; and at 54-, 67-, 85-, and 116-m heights at LLLJP site. The vertical dashed lines in the
 

upper row represent the nominal rated wind speeds and those in the lower row represent the
 

Figure 7-28. Variations of IAT and Ncoh with height and local U velocity and RiTL at LLLJP site.
 

The horizontal red line represents a nominal turbine rated wind speed of 12.5 m s–1 and the
 

Figure 7-29. Observed variation of maximum Tcoh as function of height for California wind farm, 

67-, 85-, and 116-m heights on LLLJP 120-m turbine at 1700–0800 LST (0000–1500 UTC). The
 

three turbine response thresholds measured on the Micon 65/13 turbines and the ART are shown 

Figure 8-2. Observed LLLJP probability distributions of peak Ecoh over 54- to 116-m layer. The
 

Figure 8-4. Observed LLLJP probability of hub-height peak Ecoh within the CRR range. The
 

dynamic response thresholds from the Micon turbines and the ART are shown as vertical dashed 

Figure 8-5. Observed LLLJP percentile probability distributions key scaling and turbulence
 

parameters associated with turbine dynamic response for reduced analysis data set by stability
 

Figure 8-6. Observed LLLJP percentile probability distributions of variation by stability class of
 

buoyancy length scale Lb in (a) upper half rotor disk (85–116 m) and (b) lower half (54–85 m). 

The cross-hatched areas indicate the P25–P75 (Q1–Q3) range. The distributions of the rotor layer 

Figure 8-7. Observed peak instantaneous vertical fluxes of Ecoh as function of height across
 

Figure 8-8. Portion of fixed azimuth, vertical sector scan measured by NOAA HRDL lidar on 

September 15, 2003, 18:11:12 to 18:11:34 MST. The vertical arrows indicate strong downward 

bursts of higher velocities into the shear layer below a 20-m s–1 LLJ at about 200 m, which 

would be occupied by a GE 1.5-MW turbine rotor. There is some indication that KHI also may
 

Figure 8-9. Example of raw (circles) and smoothed (red lines) sodar-measured wind speed and 

direction profiles with the tower data used to extend lower limit to 3-m height. The rightmost
 

(Tcoh), and number of structures (Ncoh)....................................................................................... 190
 

coherent structure characteristics in Figure 7-18 ........................................................................ 191
 

Figure 7-26. NWTC measured variation of peak Ecoh with Tcoh within a 10-minute record...... 192
 

stability classifications................................................................................................................ 194
 

vertical black lines represent the stability classifications. .......................................................... 195
 

NWTC, and LLLJP sites............................................................................................................. 196
 

Figure 8-1. Diurnal distribution of observed 10-minute record peak Ecoh values measured at 54-, 

as the dashed and solid horizontal lines...................................................................................... 199
 

dot-dashed, dashed, and solid vertical lines indicate the threshold (2 m2 s

–2), moderate (5 m2 

s

–2),
 

and significant (10 m2s

–2) dynamic response levels seen on the turbines.................................. 200
 

Figure 8-3. Observed LLLJP probability distribution of RiTL for filtered data set ..................... 202
 

lines............................................................................................................................................. 202
 

class............................................................................................................................................. 203
 

peak momentum (u′w′) and buoyancy fluxes (w′T′) are shown in (c) and (d), respectively....... 204
 

WindPACT rotor disk: (a) downward and (b) upward ............................................................... 205
 

exist............................................................................................................................................. 206
 

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graph plots the measurement confidence level, a measure of the sodar signal-to-noise ratio, with 

1 being the poorest and 4 the best. The lower dot-dashed lines indicate the height range of a GE
 

1.5-MW turbine and the upper dot-dot-dashed line is an estimate of the maximum upper height 

of a future 10-MW turbine. The jet maximum was at 241 m AGL............................................ 208
 

Figure 8-10. Profiles on June 17, 2002, 1900 to 2350 LST. Jet on left (a) remained stable and did 

not break down. Jet on right (b) broke down into turbulence after 2100 LST. The lower dashed 

lines outline the height range of a GE 1.5-W turbine and the upper longer dashed line represents
 

Figure 8-11. Turbulent and background flow characteristics for June 17, 2002, morning and 

evening case studies. The hub-height (85-m) mean wind speed U and RiTL are plotted in (a) and 

(d); the hub-height σw and peak Ecoh are plotted in (b) and (e); and the disk-diameter normalized
 

Figure 8-12. Observed variations of buoyancy length scale of mean rotor disk layer with RiTL for 

Figure 8-13. NOAA HRDL lidar observations of coherent turbulent patches: (a) lidar estimated 

TKE patches in upper panel with corresponding tower measurements below; (b) same as (a) but
 

with mean wind speed U(z) profile (dot-dot-dashed line) with corresponding sodar-measured
 

wind speed and σw profiles (yellow line). Time series of the instantaneous measurements of Ecoh
 

at the four heights on the met tower are shown in the lower graph. The light dashed lines outline
 

the bottom, hub, and top of the WindPACT (GE) 1.5-MW turbine rotor. The minimum threshold 

and the moderate dynamic response levels are shown in the lower graph of (b) as horizontal
 

Figure 8-14. Time series of tower-measured instantaneous Reynolds stress components and Ecoh
 

values corresponding to HRDL profiles in Figure 8-13 between 330 and 480 seconds. Individual
 

coherent structures are indicated by dashed lines marked (a–f) and vertically correlated structures
 

Figure 8-15. Time series plots of instantaneous local values of buoyancy flux ' '

a possible maximum height of a 10-MW turbine. ...................................................................... 209
 

buoyancy length scale Lb /D and the turbine layer buoyancy frequency Nbuoy in (c) and (f). .... 211
 

0010 to 0400 LST and 1900 to 0000 LST on June 17, 2002...................................................... 212
 

dashed lines................................................................................................................................. 214
 

are indicated by the rectangle identified as (g). .......................................................................... 215
 

wT and Ecoh for 

330 and 480 seconds in Figures 8-13 and 8-14. The same coherent structures identified in Figure 

8-14 are marked with the same letters. The effects of turbulent damping can be seen on each of
 

the identified individual structures.............................................................................................. 216
 

Figure 8-16. Observed frequency distributions of (a) lowest jet heights and (b) corresponding
 

Figure 8-18. Observed variation of wind speed of lowest LLJ height for Lamar site for May–
 

November 2002........................................................................................................................... 220
 

Figure 8-19. Probability distributions of variations of wind direction shear from 50 m to height of
 

Figure 8-20. Available distributions of (a) stability classes; and (b) hub-height mean wind speeds
 

by stability class with coherent structure (w/CS) and without (wo/CS) within the rotor layer.
 

Rated wind speeds for the WindPACT and NREL 5-MW Reference turbines are indicated by
 

Figure 8-21. Monthly IQR distributions of (a) and (b) RiTL; and (c) and (d) hub-height mean 

wind speed U. The low-level jet warm season is highlighted in red. The stable stability classes
 

are annotated in red in (b) and the rated wind speeds for the WindPACT and NREL 5-MW
 

wind direction for May–November 2002 at Lamar site.............................................................. 218
 

Figure 8-17. Probability variations of maximum velocities of lowest jets with height.............. 219
 

the lowest jet: (a) probability and (b) cumulative probability .................................................... 221
 

blue dashed and dot-dot-dashed lines, respectively.................................................................... 224
 

Reference turbines are shown as dashed lines in blue in (c) and (d). ......................................... 225
 

xxvii 
 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 9-1. Estimated values of rotor disk layer average stability parameter z/LMO as function of
 

RiTL. The NWTC and Lamar relationships were empirically determined from direct
 

measurements of local values of z/LMO and RiTL at these two sites. The vertical dashed line at
 

RiTL = +0.10 corresponds to the nominally upper limit of turbine dynamic response seen on the
 

Figure 9-2. (a) Variation of NWTC ART rotor disk average value of local u* (u*D) with diabatic
 

Figure 9-4. Variation of rotor disk layer mean value u*D with surface value u*o for all cases
 

(black line), with coherent structures at all heights (red line), and with no coherent structures at
 

any height within rotor disk layer (white dashed line). The dashed blue line is the best fit curve
 

Figure 9-5. Lamar site variation of local stability parameter z/L and z/LD with z/Lo by height. 

Figure 9-6. Variations of resolved turbulence high and low cyclic frequency spectral peaks
 

upwind of Row 1 and downwind of Row 41 of California wind farm environment with Micon 

65/13 RiTL. Horizontal dashed line represents 1/rev cyclic frequency. The CRR and CRRH
 

Figure 9-7. Same as Figure 9-6, but spectral peaks are scaled with equivalent Micon 65/13 rotor
 

Figure 9-8. Same as Figure 9-6, but for NWTC ART and virtual WindPACT turbine in Lamar
 

Figure 9-9. Same as Figure 9-8, but spectral peaks are scaled in equivalent rotor diameters for
 

Figure 9-10. Example of turbulent component logarithmic spectral variations with stability for
 

wind farm models (WF_UPW, WF_7D, and WF_14D). The WF_7D model uses the same
 

spectral distribution as the WF_14D model, and therefore the plotted spectra for these two 

positions in the wind farm are identical because a common value of u* was used to scale all three 

Figure 9-11. Comparison of variation of turbulent component logarithmic frequency spectra with 

stability for hub height of 80 m, Uhub = 15 m s–1, and u*D = 1.1 m s–1 for (a) NWTCUP and (b) 

Figure 9-13. Variations of equivalent wavelengths of high-frequency turbulence component
 

Figure 9-14. California wind farm variations of ratios of σu , σv , and σw with hub u* and σv /σu
 

, σw /σu with stable stability for (a) upwind of Row 1; and (b) upwind of Row 37 (7D) and 

Figure 9-15. Variation of ratios of σu , σv , and σw with hub u* and σv /σu , σw /σu with stable
 

Figure 9-16. Observed turbulence component cross-correlation coefficient probability
 

distributions (ruw, ruv, and rvw) for 23-m hub height at three locations at wind farm, three heights
 

within ART rotor disk on Row 4 of NWTC, and at five heights within virtual WindPACT 1.5­

Micon turbines and the ART....................................................................................................... 229
 

surface value, u*o; (b) probability density distribution of u*D – u*o.......................................... 233
 

Figure 9-3. Probability density function of z/LD – z/Lo difference for NWTC ART rotor disk . 234
 

for all cases. ................................................................................................................................ 236
 

Horizontal and vertical dashed lines outline observed z/L value range of ±1. ........................... 237
 

stability class boundaries are shown as vertical dashed and dotted lines, respectively.............. 239
 

diameter for rated wind speed conditions ................................................................................... 240
 

site environment.......................................................................................................................... 242
 

rated wind speed conditions........................................................................................................ 243
 

models......................................................................................................................................... 244
 

GP_LLJ models .......................................................................................................................... 245
 

Figure 9-12. Comparisons of TurbSim model turbulent component spectra for hub height of 80 

m, Uhub = 15 m s–1 , u*D = 1.1 m s–1: (a) RiTL = –0.05; (b) RiTL = 0; (c) RiTL = +0.05 .............. 247
 

spectral peaks with RiTL. San Gorgonio WF_7D and WF_14D spectral models scaled with the
 

hub height of 23 m, Uhub = 12 m s–1, and u* = 1 m s–1. .............................................................. 248
 

downwind of Row 41 (14D) ....................................................................................................... 249
 

stability for (a) TurbSim SMOOTH and (b) NWTCUP spectral models ................................... 250
 

MW turbine rotor disk layer at Lamar site.................................................................................. 253
 

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Figure 9-17. Available population Reynolds stress component residual distributions for hub 

heights at (a) wind farm; (b) ART; and (c) Lamar site (virtual WindPACT 1.5-MW turbine). 

Dashed lines represent the Gaussian distributions for the observed residual populations. ........ 257 

Figure 9-18. Variation of coherent decrement “a” with height and RiTL for mean wind speed 

range of 12–14 m s–1 for (a) NWTC ART and (b) Lamar site (WindPACT 1.5-MW turbine).. 259 

Figure 9-19. Variation of U-component coherence decrement “a” and offset term “b” normalized 

by Lu integral length scale by stability class and hub mean wind speed: (a) NWTC ART and (b) 

Lamar site (WindPACT 1.5-MW reference turbine).................................................................. 260 

Figure 9-20. Same as Figure 9-19, but for V-component ........................................................... 261 

Figure 9-21. Same as Figure 9-19, but for W-component........................................................... 262 

Figure 9-22. Variation of U- and V-component coherence decrement “a” and b offset term 

normalized by integral length scale L for California wind farm upwind of Row 1 and at Rows 37 

and 41. Vertical component coherence scaling was unavailable because of a lack of vertical 

velocity measurements................................................................................................................ 263 

Figure 9-23. Same nomenclature as Figures 8-13a and 8-14 of (a) specially processed HRDL 

lidar “stare” observation with tower-measured Ecoh in lower panel; and (b) corresponding towermeasured time series for subperiod of 330–480 seconds of Reynolds stress components and Ecoh. 

Individual (a–f) and regions (g) of coherent structures are outlined by the dotted lines............ 265 

Figure 9-24. Observed probability distributions of turbulence scaling parameters associated with 

coherent turbulent structures occurring simultaneously at all available measurement locations for 

ART upwind planar array and Lamar site 120-m met tower. The distributions of RiTL are shown 

in (a) NWTC and (b) Lamar. The distributions of the equivalent hub-height mean U speed are 

plotted in (c) NWTC and (d) Lamar. .......................................................................................... 267 

Figure 9-25. Same as for Figure 9-24, but for rotor disk mean shear stress u*D: (a) NWTC and 

(b) Lamar; and rotor layer mean shear ∂U / ∂z across respective ART and WindPACT rotor  D 

diameters: (c) NWTC and (d) Lamar.......................................................................................... 268 

Figure 9-26. Probability density distribution of observed Tcoh at hub height for the wind farm 

measurement locations within the California wind farm............................................................ 269 

Figure 9-27. Example of background (U, V, W) plus added coherent structure wind components 

(u', v', and w'): streamwise (U + u'), crosswind (V + v'), and vertical (W + w') at specific grid 

point location .............................................................................................................................. 272 

Figure 9-28. Example of a TurbSim NWTCUP spectral model simulation with and without 

coherent turbulent structures (CS) added. Light gray shows significant (~450 seconds) but fewer 

CS generated within the background flow compared with the CS added (~90 seconds). .......... 272 

Figure 9-29. Probability distributions of Lamar site LLJ characteristics with height: (a) time 

period; (b) wind direction at LLJ maximum; and (c) wind speed of LLJ maximum for the 

STC02, STC03, STC04, and STC05 stability classes. The largest turbine dynamic responses 

occur in the STC03 class. The boxplot dots represent the P05 and P95 percentiles. ................. 274 

Figure 9-30. Probability distributions by stability class of WindPACT (GE) 1.5-MW rotor layer 

turbulence scaling parameters for corresponding LLJ heights: (a) z/LD; (b) u*D; and (c) ∂U / ∂z .  D 

..................................................................................................................................................... 275 

Figure 9-31. . Vertical profiles of the median: (a) LLJ peak UH and corresponding wind 

direction WD; (b) RiTL and rotor disk layer mean z/L; (c) rotor disk layer mean u* and ∂U / ∂z  

for subset of sodar vertical profiles that reached 500 m. ............................................................ 276
 

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Figure 9-32. Observed Lamar site maximum LLJ velocities with height .................................. 278
 

Figure 9-33. GP_LLJ model profile variations for 80-, 260-, and 460-m jet heights with
 

variations in U jet max and RiTL values of +0.50 and +0.05. The three lower dashed lines represent 

the rotor disk layer and hub height of the WindPACT 1.5-MW turbine and the upper is an 

approximate maximum elevation of a 10-MW turbine rotor...................................................... 279
 

Figure 9-35. GP_LLJ model profile variations for 80-, 260-, and 460-m jet heights with
 

Figure 9-36. Examples of three TurbSim GP_LLJ spectral model LLJ wind speed and direction 

profiles for 80-m mean wind speed of 12 m s–1 and RiTL of +0.05. The wind direction is relative
 

Figure 9-37. TurbSim simulation of NWTC LIST ART inflow observation of December 15, 

2001, at 0736 MST. Isocontours of simulated Ecoh (a) without coherent structures and (b) with 

Figure 9-38. TurbSim simulation of intense LIST ART inflow turbulence observation, February
 

Figure 9-39. TurbSim GP_LLJ spectral model simulation of inflow Ecoh to NREL 5-MW
 

Reference turbine without LLJ and no coherent structures: (a) –5 to +50 seconds and (b) 125- to 

Figure 9-40. Statistical comparisons of observed probability distributions of P05–P95 range
 

observed hub-height u* and peak Ecoh with stability and mean wind speed classes with NWTCUP
 

and GP_LLJ TurbSim simulations using observed median values for boundary conditions: (a)
 

Figure 9-41. Same as Figure 9-40, but observed hub-height σu, σv, and σw with NWTCUP and
 

GP_LLJ TurbSim simulations using observed median values for boundary conditions: (a)
 

Figure 9-42. Same as Figure 9-40, but for observed hub-height mean u'w', u'v', and v'w' Reynolds
 

stresses with NWTCUP and GP_LLJ TurbSim simulations using observed median values for
 

Figure 9-34. GP_LLJ model profile variations for 80-, 260-, and 460-m jet heights with
 

variations in RiTL and u*D values of +0.2 and +0.6 m s–1........................................................... 280
 

variations in u*D and RiTL values of +0.50 and +0.05 ................................................................ 281
 

to the direction at 80 m. .............................................................................................................. 282
 

coherent structures. ..................................................................................................................... 284
 

5, 2001, 0505 MST: (a) without coherent structures and (b) with coherent structures .............. 286
 

225-second periods ..................................................................................................................... 287
 

NWTCUP and (b) GP_LLJ......................................................................................................... 289
 

NWTCUP and (b) GP_LLJ......................................................................................................... 290
 

nine boundary conditions: (a) NWTCUP and (b) GP_LLJ ........................................................ 291
 

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List of Tables 

Table 1-1. SeaWest Micon 65/13 Turbine Specifications .............................................................. 3
 

Table 3-1. Correlation of Loading Distribution Model Shape Parameters with Turbulence
 

Table 7-6. Statistics of Matched Micon 65/13 Turbine Responses, Turbulence Scaling
 

Parameters, and Corresponding Coherent Structure Attributes for Peak Ecoh > 5 m2 s

–2 and NREL
 

Table 7-7. Inflow Turbulence Parameters and Coherent Structure Characteristics from San
 

Table 8-1. Distributions of LLLJP Nocturnal Data Records by Stability Class after Applying
 

Table 9-1. Mean Reynolds Stress Scaling Magnitudes Sensitivities at Wind Farm Locations with
 

Table 9-2. Sensitivities of Mean Reynolds Stress Component Magnitudes to Turbine Layer
 

Table 9-3. Sensitivities of Mean Reynolds Stresses Magnitudes to Turbine Layer Turbulence
 

Table 9-4. Scaling of Expected Length of Coherent Structures (Tcoh) within a Simulated Record
 

Table 9-5. Coherent Structures Maximum Intensity (Peak Ecoh) Scaling Parameter Sensitivities
 

Table 9-6. Coherent Structures Interarrival Time (1/λ) Scaling Parameter Sensitivities by
 

Parameter Predictors ..................................................................................................................... 29
 

Table 3-2. Cross-Correlation Coefficients for Inflow Turbulence Parameters with FBM DELs. 43
 

for Values > 0.3 ............................................................................................................................ 43
 

Table 6-1. Turbine Layer Stability Classifications for Turbine Response Correlations............. 122
 

Table 7-1. WindPACT Turbine Calculated Static System Frequencies..................................... 158
 

Table 7-2. Calculated WindPACT Baseline Turbine System Nonrotating Modal Frequencies. 159
 

Table 7-3. CART2 (ART) Measured and Calculated Static System Frequencies...................... 172
 

Table 7-4. CART2 (ART) System Nonrotating Modal Frequencies.......................................... 173
 

Table 7-5. NREL 5-MW Reference Turbine Nonrotating System Modal Frequencies ............. 177
 

Rotor FBM DEL > P90 (18.95 kNm) ......................................................................................... 182
 

Gorgonio Row 37 Data Set for 0.95 < Lb/Dnrel < 1.05 ............................................................... 188
 

Described Constraints ................................................................................................................. 198
 

Turbine Layer Turbulence Parameters........................................................................................ 254
 

Turbulence Scaling Parameters in NWTC Row 4 ...................................................................... 255
 

Scaling Parameters at Lamar Site ............................................................................................... 256
 

by Location ................................................................................................................................. 269
 

by Location ................................................................................................................................. 270
 

Location ...................................................................................................................................... 270
 

Table 9-7. Wind Speed Bin Classification.................................................................................. 288
 

xxxi 
xxxii
 
 

 

 

 

 

 

 

 

 

 

1.0 Introduction 

Between 1975 and 1985, the U.S. Department of Energy (DOE) either directly sponsored or 

supported the development of a series of utility-scale wind turbines ranging in generating 

capacity from 200 kW to 4 MW. This work was conducted under the auspices of the Federal 

Wind Program. The Lewis (now Glenn) Research Center of the National Aeronautics and Space 

Administration (NASA) managed the utility-scale turbine development program for DOE in 

which a series of horizontal axis wind turbine (HAWT) prototypes with increasing generating 

capacity were designed, constructed, and operated by several contractors, including 

Westinghouse, General Electric, and Boeing Engineering and Construction. 

The “MOD” series of turbines developed under the Federal Wind Program included the 200-kW 

MOD-0A, the 2-MW MOD-1, the 2.5-MW MOD-2, and the 3.2-MW MOD-5B prototypes. The 

Hamilton-Standard Division of United Technologies, with support from DOE and NASA, 

developed a prototype 4-MW turbine (WTS-4) for the U.S. Bureau of Reclamation as a “system 

verification unit.” The performance of this turbine was evaluated as a potential component in the 

integration of large-scale wind power generation with the existing hydropower system in the 

western United States. At the same time, Sandia National Laboratories (SNL), also under the 

sponsorship of the Federal Wind Program, was developing a series of utility-scale vertical axis 

wind turbine (VAWT) prototypes that culminated in a 600-kW prototype design with an 

equatorial diameter of 34 m. 

Although significant knowledge was gained from this range of turbine designs, only one of the 

original prototypes was produced commercially. Westinghouse constructed fifteen 600-kW 

turbines that were largely based on the MOD-0A prototype. These were installed on the 

northeast coast of the Hawaiian island of Oahu. The DOE/NASA 3.2-MW Boeing MOD-5B 

prototype was also installed nearby. Both turbines suffered chronic underproduction issues with 

significant numbers of faults and failures that occurred predominately at night. The MOD-5B 

also experienced serious structural loading issues when the normally onshore and upsloping 

winds reversed and descended from the higher terrain to the west and southwest (downslope 

winds known locally as Kona winds). These particular wind conditions induced unacceptable 

vibration levels in the turbine structure, and the turbine then had to be shut down. During the 

same period, an unrelated commercial wind farm consisting of small 17.5-kW and 20-kW 

turbines installed on high terrain near the northernmost point of the island of Hawaii was 

suffering a significant numbers of failures that occurred exclusively at night. 

Analyses of the performance of these prototype turbines found that the structural fatigue damage 

they sustained during their operation in various environments far exceeded the original design 

estimates in virtually all cases. These excessive loads were attributed to the impact of 

atmospheric turbulence. 

As turbine sizes have grown and turbines with capacities at or exceeding the earlier 

multimegawatt prototypes have been constructed, many of the issues seen with the earlier 

designs have reappeared. Although the current generation of turbines was designed keeping in 

mind the earlier problems, today’s more structurally flexible and taller turbines are now 

penetrating deeper into the planetary boundary layer. This has led to much higher than 

anticipated maintenance and repair costs and reduced capacity factors. Statistical studies of the 

1
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

productivity and operating costs of the current fleet of wind farms have shown systemic power 

underproduction exacerbated by the higher than expected maintenance and repair costs. Turbine 

availability is estimated to account for almost half of this loss, of which downtime for repairs are 

a major constituent. The cumulative nature of the turbine lifetime trend in maintenance and 

repair costs strongly suggests that the environments used to design wind turbines are deficient. 

We offer evidence in this report that critical turbulent conditions are either being missed or 

inadequately applied when new turbine designs are being developed, which is contributing to 

current performance issues. 

1.1 Inflow Turbulence and Turbine Response Research

In 1989, the Wind Technology Group at the National Renewable Energy Laboratory (NREL) 

began a DOE-sponsored program to develop a physical understanding of the role of atmospheric 

turbulence in the dynamic response of wind turbines. The initial objective was to gain a detailed 

understanding of the physics of the interaction of atmospheric turbulence and the resulting 

dynamic loading induced on turbine components. The next step was to quantify that interaction 

with the dominant turbulence scaling parameters and their influence on the structural response 

and corresponding fatigue damage to wind turbine components. This is best accomplished by 

simultaneously measuring the microscale characteristics (time and space scales of wind field 

motions smaller than the turbine rotor diameter) of the turbulence as it enters the turbine rotor 

and the resulting dynamic loading response of key turbine components such as the blades, 

drivetrain, and tower. 

1.2 Field Measurements of Turbine-Turbulence Interactions 

Such valuable information was collected and analyzed during two major field experiments 

conducted on operating turbines between 1989 and 2000. The purpose of the field experiments 

was to identify the inflow turbulence characteristics associated with the greatest dynamic 

response, which was therefore creating the largest fatigue loads. The analysis of these two field 

measurement campaigns gave us detailed insight into the turbulence characteristics. We used this 

information when developing the TurbSim stochastic turbulence simulator code and made sure to 

include the inflow conditions responsible for the most damage. Our research has been built on 

the foundation of Paul Veers’ pioneering stochastic turbulence simulation work at SNL. 

During June, July, and August of 1989 we took continuous turbulence measurements from the 

two 50-m (164-ft) met towers installed upwind and downwind of a 41-row wind farm consisting 

of almost 1,000 turbines located east of San Gorgonio Pass in Southern California (California 

wind farm). The following year and over the same period we collected the first timesynchronized inflow turbulence and dynamic response data from two adjacent 65-kW wind 

turbines located in Row 37 of this same wind farm. The second major turbulence-turbine 

interaction experiment took place in 1999–2000 at the National Wind Technology Center 

(NWTC) near Boulder, Colorado, using a 600- kW two-bladed upwind turbine operating in the 

natural but energetic turbulent flow identified with this site. This experiment was unique in that 

the inflow to the turbine was measured by five ultrasonic anemometers/thermometers mounted as 

a planar array upwind of the turbine rotor. The spacing of these anemometers was the same as 

the rotor height and diameter. 

2
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.3 San Gorgonio Pass Wind Farm Experiment

In 1989 we entered into a cooperative agreement with the large wind farm operator SeaWest. 

The agreement allowed us to make turbine dynamics and turbulence measurements at their San 

Gorgonio wind farm near Palm Springs, California. SeaWest made two Micon 65/13 turbines on 

Row 37 available to NREL, enabling us to compare the performance of a set of newly designed 

rotor blades (NREL thin airfoil) on one turbine with a neighboring machine equipped with a set 

of refurbished original equipment (AeroStar) blades (see Tangler et al. [1991] for details). 

1.3.1 The Turbines and Local Inflow Instrumentation 

The Micon 65/13 turbine is an upwind, three-bladed machine that is stall regulated with a hub 

height of 23 m. Both turbines had a rotor speed of 48 rpm and an induction-type generator (65/13 

kW). Table 1-1 summarizes the Micon 65/13 turbine specifications. Figure 1-1 illustrates the 

measurement layout. 

Table 1-1. SeaWest Micon 65/13 Turbine Specifications 

Characteristic AeroStar Rotor Equipped NREL Rotor Equipped 

Rotor diameter 16.0 m 17.0 m 

Blade length 7.4 m 7.9 m 

Airfoils NACA 4415-24 S806A, S805A,S807a 

Blade weight 363-386 kg 286 kg 

Peak power 70 kW @ 15.2 m s –1 65 kW @ 12.5 m s –1 

a

Source: Tangler and Somers (1995) 

NACA = National Advisory Committee for Aeronautics 

Each turbine had an extensive and identical complement of instrumentation, including strain 

gauges to measure out-of-plane (flapwise) and in-plane (edgewise) blade root bending loads on 

each blade, tower bending loads at several locations, and orthogonal low-speed shaft bending 

loads. Force-balance, two-axis accelerometers installed in the turbine nacelles measured the 

vibration environment and thrust loads parallel and lateral to the low-speed shafts. A local 31-m 

met tower (shown in Figure 1-1) was installed 1.5 rotor diameters upwind of and between the 

two turbines. It was equipped with three levels of propeller vane anemometers over the height 

range defined by turbine rotor disks, an ultrasonic anemometer/thermometer near hub height, 

mechanically aspirated platinum resistance temperature measurements near the surface and at the 

top of the tower, and barometric pressure measurements using a digital micro barometer at a 2-m 

height. Figure 1-2 displays the measured power curves for the two Micon turbines derived from 

the available data. 

3
 
 

 

Sources: (a) James Tangler, NREL; (b) and (c) Warren Gretz, NREL 

Figure 1-1. Row 37 of California wind farm: (a) looking downwind at the two test turbines 

(AeroStar rotor-equipped on the left, NREL rotor-equipped on the right) with the upstream met 

tower; (b) looking upstream (westward) from Row 37 at sunset; (c) looking north with NREL data 

trailer at Row 38 

4
 
Figure 1-2. California wind farm Micon 65/13 turbine power 

curves 

5 
 

1.3.2 The Upwind and Downwind Met Towers 

SeaWest also supported NREL in installing two 50-m (167-ft) meteorological measurement 

towers upwind of Row 1 and downwind of Row 41 at the wind farm. Figure 1-3 depicts the 

general area surrounding the wind farm and the location of the 50-m towers used in 1989. The 

flow emanating from San Gorgonio Pass to the west is channeled into the wind farm by the 

higher terrain on each side. Two side-by-side test turbines on Row 37 were employed in the 1990 

experiment. Each 50-m tower up and downwind was equipped with the following: 

	 A three-axis ultrasonic anemometer mounted at the nominal wind farm turbine hub height 

of 23 m 

	 Three levels of very sensitive wind speed and direction sensors 

	 Platinum resistance temperature sensors at 5- and 50-m heights 

	 A lithium chloride/platinum resistance temperature detector (LiCl/PRTD) dew point 

temperature sensor at 5 m 

	 Barometric pressure at a height of 2 m. 

Source: U.S. Geological Survey 

Figure 1-3. Terrain characteristics surrounding California wind farm. The approximate shape of 

the farm is shown with the locations of the upwind and downwind 50-m met towers and the two 

test turbines at Row 37. 

6 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.3.3 Synopsis of San Gorgonio Wind Characteristics

The primary wind season in the San Gorgonio Pass area is between April and September, when 

the largest temperature difference exists between the marine air over the Pacific Ocean to the 

west and the hot, dry air over the Mohave and Sonoran deserts to the east. This air 

temperature/density difference is responsible for the development of a strong horizontal pressure 

gradient as cooler, denser air accelerates through the pass toward the low pressure over the desert 

that results from intense convectional heating. Wind speeds east of the pass tend to peak from 

July through early August, when the desert surface temperatures reach a maximum and produce 

the continuous convectional heating, which maintains a consistent low pressure over the entire 

diurnal period. East of the pass, where the wind farm is located, the wind speeds often decrease 

significantly in the middle of the day (between 1000 and 1500 local time). This wind pattern 

results from strong rising air currents associated with the intense midday convectional heating. 

These currents are a barrier to the western flows entering the wind farm. During the 2-year span 

of these experiments, the turbines on the western side of the wind farm often operated in light 

westerly winds and those in the easternmost few rows faced in the opposite direction due to the 

southeasterly flow there. In between, the winds were often calm or at least well below cut-in 

speed, so little or no power was being generated in this portion of the wind farm. This was true 

of the two turbines being tested at Row 37. Figure 1-4 shows the diurnal variation of the hourly 

percentiles of the hub-height mean wind speed (U H ) measured at Row 37 during the 

experiment. 

-1 ms 

16 

14 

12 

10 

8 

6 

4 

0 2 4 6 8 10 12 14 16 18 20 22 

P99 

P95 

P90 

P75 

P50 

P25 

P10 

P05 

P01 

NREL rotor rated wind speed 

sr ss 

Local standard time (h) 

Figure 1-4. Diurnal variation of hourly percentiles of hub-height mean wind speed U H 

(distributions from test of Micon 65/13 turbines at Row 37 of wind farm in 1990. The rated wind 

speed for the Micon 65/13 turbine with the NREL rotor is shown as a horizontal dashed line. Local 

sunrise (sr) and sunset (ss) for mid-July 1990 are shown as vertical dash-dot-dotted lines. The 

strongest winds typically occurred around 2200 local standard time (LST). 

7
 
 

 

 

 

 

 

 

 

 

 

1.4 NWTC Experiments

We had the opportunity in 1999–2000 to extend the work begun with the two California Micon 

turbines using the 600-kW Advanced Research Turbine (ART) installed at the NWTC. It was 

part of the Long-Term Inflow and Structural Test (LIST) Program performed in collaboration 

with SNL. Though somewhat smaller in comparison with the commercial turbines being 

installed at the time, the ART was large enough to study the turbine dynamic response from the 

spatial turbulent inflow into a rotor that was twice the size of the Micon turbines. Although not 

exposed to an internal flow field within a multirow wind farm, the NWTC’s natural turbulence 

characteristics are known to be very energetic because of the strong, turbulent downslope winds 

from the Front Range of the Colorado Rocky Mountains to the west. 

The size of the ART allowed us to construct an upwind planar array of ultrasonic 

anemometers/thermometers and other instrumentation scaled to the turbine rotor diameter to 

measure the spatial aspects of the turbulent inflow. SNL constructed a similar array in upwind of 

a modified Micon turbine (referred to as a Micon 65/13M) that was installed at a Great Plains 

site near Bushland, Texas, as another element of the LIST Program (Sutherland 2002). 

1.4.1 The ART 

The ART is a Westinghouse WWG-0600 600-kW turbine that was constructed in the early 1980s 

and originally installed and operated on the island of Oahu in Hawaii before being relocated to 

the NWTC. During the LIST experiment it was operated in its original configuration as a twoblade, upwind machine with a 42-m-diameter rotor. It incorporated a synchronous generator and 

full span pitch control to regulate power and maintain a constant rotational speed of 43 rpm. The 

power generating range was from 6.3 m s

–1 at cut-in to 22.3 m s–1 at cutout with rated power 

attained at 12.8 m s

–1 . The turbine has since been retrofitted with a three-blade rotor, powerful 

electric blade pitch actuators, variable speed power regulation, and a highly programmable 

digital control system for use in advanced controls research. It is now referred as the Controls 

Advanced Research Turbine 3 (CART3). A second nearby Westinghouse turbine had been 

previously modified for variable speed controls research with the original two-blade 

configuration, and it is referred to as the CART2. 

Figure 1-5 shows the NWTC and the locations of the ART and the CART2 as they existed 

during the LIST experiment (1999–2000). A schematic representation of the upwind planar 

measurement array is shown at its approximate position upwind of the ART. The immediate 

upwind fetch is relatively flat and homogenous with the surface elevation increasing slightly in 

the nominal prevailing wind direction towards the west boundary of the NWTC site. El Dorado 

Canyon is shown on the upper left. The flow out of this canyon has a significant influence on the 

wind conditions at the NWTC. 

8
 
 

 

 

 

 

 

 

Nov 1999-May 2000 

ART 

CART2 

Source: NREL PIX 12586 

Figure 1-5. NWTC, location of the ART, and approximate position of upwind planar array of five 

sonic anemometers and other meteorological instrumentation 

1.4.2 A Synopsis of NWTC Wind Conditions

The NWTC sits along the mountain–plains interface immediately east of the Front Range 

Mountains, as shown in Figure 1-6. The elevations of the mountaintops along the Continental 

Divide about 40 km to the west average 3,800 m (12,500 ft) above mean sea level (MSL). The 

elevation of the NWTC property is 1,841 m (6,040 ft), a drop of more than 2,200 m (6,500 ft) 

from the highest terrain to the west. El Dorado Canyon channels high speed flows descending in 

the lee of the mountains onto the property (see Banta et al. 1995). Figure 1-7 displays an eastwest cross section through Boulder of the predicted flow over the Front Range Mountains and a 

moderate downslope event to their lee. The location of the NWTC is approximately shown 

immersed in the warmer, drier, and stronger wind flow near the ground. The wind arrows also 

indicate the significant downward wind component at the foot of the mountains. 

The winds associated with the downslope flows at the NWTC have a distinct pulsating 

characteristic: the wind speeds can vary over a very wide range in a few minutes. In addition to 

being very gusty, these winds contain high levels of turbulent energy. Based on 9 years of 

record, Figure 1-8a shows the distributions of streamwise turbulence intensity ( σ / U ) as a 1 

function of the 80-m mean wind speed. The width of the box corresponds to the 25% and 75% 

quartiles. The solid black indicates the median and the solid red the mean. The length of the 

whiskers represents the P10 and P90 percentiles and the filled circles represent the observations 

less than P05 and greater than P95 (outliers). The specified relationships between turbulence 

intensity and mean hub-height wind speed for the three International Electrotechnical 

Commission (IEC) turbulence classes (A, B, and C; see IEC [2005]) are also shown. The 

turbulence intensities near typical rated wind speeds (11–13 m s

–1) are often significantly greater 

than even the most turbulent IEC Class A. Figure 1-8b plots the distributions of the standard 

deviation of the streamwise wind component. 

9
 
 

 

 Source: U.S. Geological Survey 

Figure 1-6. Topography upwind of NWTC. The inset shows the topography cross section along the 

prevailing wind direction (dashed line).

 Source: Courtesy of the Research Applications Laboratory of the National Center for Atmospheric Research 

Figure 1-7. East-west vertical cross section through Boulder, Colorado, from 20-km resolution 

Weather Research and Forecasting (WRF) model operational prediction for 1500 GMT on January 

13, 2011. The arrows parallel the wind flow and their length is proportional to the speed. The solid lines 

indicate the potential temperature. The shaded areas represent relative humidity, with the highest values 

in darkest green. The approximate position of the NWTC is shown. A moderate downslope wind event is 

forecast with warmer and drier air being brought down by the indicated winds. 

10 
0.6 

Class A 

Class B I 80 0.5 Class C 

 P05 < I80 > P95 

0.4 

0.3 

0.2 

0.1 

0.0 

(a) 

3 5 7 9 11 13 15 17 19 21 23 25 27 29 

U ms 80 ( / )

10 

8 



1 ˆ

P05 < 150 > P95 IEC ETM 

6 

4 

2 

(b) 

0 

3 5 7 9 11 13 15 17 19 21 23 25 27 29 

U m 80 ( / s) 

Figure 1-8. Observed NWTC box-plot probability distributions of 80-m (a) turbulence intensity, I80, 

and (b) U-component standard deviation, 1 or σu

In this figure, filled circles represent the observations less than P05 and greater than P95 

(outliers). To demonstrate the severity of this site, the specified relationship between  ( ) 1 u and 

the hub-height mean winds for the IEC Extreme Turbulence Model (ETM) is also plotted in this 

  (m/s) 1 80

11 
 

 

 

 

 

 

 

 

-

 

 

figure. Below mean wind speeds of about 17 m s

–1, an increasing number of events exceed the 

ETM criteria. 

1.4.3 ART Upwind Planar Inflow Measurement Array

To obtain information about the spatial aspects of the turbulent inflow that was not readily 

apparent in the measurements on the California Micon 65/13 turbines, we constructed the planar 

array of five ultrasonic anemometers/thermometers on the three towers shown in Figure 1-9. The 

array was installed perpendicular to the prevailing wind direction (292 degrees) 65 m (213 ft) 

upwind of the ART rotor plane. The ultrasonic anemometers/thermometers were three-axis Kaijo 

Model DAT-600s, which have a 10-Hz measurement bandwidth and velocity and temperature 

maximum resolutions of 0.002 m s–1 and 0.003°C, respectively. In addition to the ultrasonic 

anemometers, cup anemometers and wind vanes were installed at three heights on the central 

tower, along with PRTDs in both absolute and differential configurations, a digital 

microbarometer for measuring surface barometric pressure, and an LiCl/PRTD hygrometer for 

measuring the surface dew point temperature. All data channels were recorded at 40 samples per 

second. During post-processing, all but the sonic anemometer velocity and temperature 

measurements were smoothed to one sample per second. 

T 

∆Τ 

, DP, BP 

BPBP 

FT 

FT 

cup 

anemometer 

hi-resolution 

sonic 

anemometer/thermometer 

wind 

vane 

T temperature 

DP dew point temperature 

∆Τ temperature difference 

FT fast-response temperature 

BP barometric pressure 

Legend 

3 axis sonic anemometers/thermometers 

Photo source: N. Kelley, NREL 

Figure 1-9. Upwind planar measurement array used for measuring turbulent inflow to NWTC ART. The 

maximum and minimum heights were 58 and 15 m, with the left, center, and lateral measurements at the hub height of 

37 m and spaced 21 m apart. The array was located 65 m upwind of the turbine rotor plane. 

12
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.5 The Lamar Low-Level Jet Program (LLLJP) 

The LLLJP, although not using an operating wind turbine as did the California wind farm and 

NWTC experiments, was performed to obtain detailed information about the turbulence 

conditions in the atmospheric layer beneath nocturnal low-level jet streams (LLJs), a portion of 

which would be occupied by 106 Enron (now GE) 1.5-MW wind turbines. The LLLJP was 

established in the late summer of 2001 as joint effort between the NWTC and Enron Wind. 

NREL’s purpose was to gather the information that we used to develop the Great Plains LowLevel Jet (GP_LLJ) spectral model in NREL’s TurbSim. 

Enron installed a 120-m (400-ft) met tower at the site of a planned wind farm development about 

32 km (20 miles) south of Lamar, Colorado, in southern Prowers County. NREL instrumented 

that tower with several levels of sensitive instrumentation to measure the turbulence 

environment. Continuous, high-speed turbulence data collection took place during the stable 

boundary layer hours of 1600 to 0800 LST between March 2002 and March 2003. In addition, 

NREL installed an acoustic wind profiler or sodar nearby to locate and quantify low-level jets 

seen over the site and correlate that information with turbulence data collected on the tower. It 

was operated during the primary low-level jet season of May through November 2002. A 

collaborative program with the National Oceanic and Atmospheric Administration’s 

Environmental Systems Research Laboratory (NOAA/ESRL) using high-resolution Doppler 

lidar (HRDL) in conjunction with the NREL tower-based measurements and the sodar was 

conducted during the first 2 weeks of September 2003. The LLLJP site is situated on a high 

plateau south of the Arkansas River Basin. Figure 1-10a shows the regional and local topography 

overviews surrounding the experimental site. Locally, as illustrated in Figure 1-11, the terrain is 

flat and homogenous but with more complex elements to the west and north (Figure 1-10b). 

1.5.1 LLLJP Measurements 

At the LLLJP site, the base of the 120-m (400-ft) tower is at an elevation of 1,357 m (4,451 ft) 

above MSL. Views of the site and the tower-mounted instrumentation, in Figures 1-11 and 1-12, 

show three-axis sonic anemometers/thermometers installed at heights of 54, 67, 85, and 116 m 

(177, 220, 279, and 380 ft). To measure wind speed and direction, cup anemometers and highly 

damped direction vanes were mounted at 3, 52, and 113 m (10, 171, and 419 ft). 

Absolute air temperatures derived from PRTDs were measured at heights of 3, 52, and 113 m 

with temperature differences measured between 52 and 83 m (272 ft) and between 83 and 113 m. 

All temperature measurements were acquired with four-wire PRTDs placed within mechanically 

aspirated radiation shields. 

Dew point temperatures were measured at 3, 52, 85, and 113 m with LiCl/PRTD dew point 

hygrometers. Barometric pressure was measured at a height of 3 m using a digital 

microbarometer pressure transducer that was connected to an external omnidirectional sampling 

head on the exterior of the building. A Scintec MFAS acoustic wind profiler or sodar was 

installed and operated 109 m (358 ft) southwest of the tower base, as shown in Figures 1-13b, c, 

and d. It was programmed to acquire vertical wind profiles with a 10-m (33-ft) vertical resolution 

from 40 to 500 m (131 to 1,640 ft). 

The NOAA HRDL installed south of the sodar operated for 2 weeks in early September 2003. 

Figure 1-14a pictures the location of the lidar with respect to the 120-m tower. Figure 1-14b 

13
 
 

 

 

 

 

 

 

shows the HRDL being used to observe the evolution of an LLJ. Figure 1-14c presents a 

processed example of such an observed LLJ evolution. 

The tower-based measurements were collected using two recording systems. A dedicated data 

logger collected a subset of the measurements at a rate of 1/s (not including the sonic 

anemometers) and saved it as statistics (means and standard deviations for wind-related 

parameters) calculated over a 5-minute period. A second computer-based system was employed 

to collect the high-resolution sonic information in addition to the other tower data. Data were 

collected at 20 samples per second on all data channels continuously each day from 1600 to 0800 

LST to observe conditions primarily in the nocturnal boundary layer. The data were processed 

using a five-pass process and placed into archives of derived parameters that included up to 

fourth order statistics. For the analyses discussed in this report, we used more than 28,000 10­

minute high-speed turbulence records collected from April 1, 2002, to March 31, 2003, and again 

from August 30, 2003, through September 16, 2003. 

14
 
(a) 

(b) 

 Source: U.S. Geological Survey 

Figure 1-10. Location of LLLJP experiment site and 120-m tower in high plains of southeastern
 

Colorado: (a) regional topography and (b) local topography
 

15 
Source: N. Kelley, NREL 

Figure 1-11. Enron (GE) Wind 120-m met tower, southeastern
 

Colorado (LLLJP site)
 

Source: N. Kelley, NREL 

Figure 1-12. Close-up of NREL turbulence-measuring instrumentation 

installed on Enron (GE) 120-m LLLJP tower 

16
 
Photos Source: N. Kelley, NREL; Diagram: D. Jager, NREL 

Figure 1-13. Instrumentation layout at LLLJP measurement site: (a) tower; (b) nearby sodar; (c) 

Scintec MFAS sodar antenna within enclosure; and (d) plan view of site layout
 

17 
 Photo Source: N. Kelley, NREL 

Figure 1-14. NOAA/ESRL HRDL lidar in operation at LLLJP site: (a) position of lidar with respect to 

120-m tower; (b) NOAA’s Robert Banta making observations; (c) vertical scans through evolving 

LLJ. The strongest winds in the last frame on the lower right would be at the top of the GE 1.5-MW 

turbine rotors now installed at this site. Wind speed scale is at the top, with negative values 

indicating the wind was coming toward the lidar. Times are in UTC (18:24:30 to 18:51:17 MST). 

18 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.0 Defining the Turbine Inflow Turbulence Characteristics 

2.1 Wind Turbine Turbulence Operating Environment

Wind turbines operate in the lowest part of the atmosphere, which is called the planetary 

boundary layer (PBL). Until relatively recently, most turbines operated in the lowest portion of 

the PBL, the surface layer (SL). In this layer, the influence of the frictional drag induced by the 

ground is most significant. The SL is characterized by a strong diurnal variation in both the 

change of wind speed with height and turbulence characteristics. It is a consequence of heat 

being added to the atmosphere during the day and removed at night. The daytime or convective 

SL is generally deeper than its nocturnal counterpart because of the intense turbulent mixing by 

large buoyant eddies. This results in vertical transport (fluxes) of heat and momentum that are 

nearly constant with height. The nocturnal SL is usually much shallower. At some point the 

surface drag may become great enough to cause the winds above to decouple and accelerate 

relative to the slower moving air near the surface, which can create significant velocity shears 

and perhaps a low-level maximum (jet) in the wind profile. The vertical distribution of 

temperature and buoyancy determines the behavior of vertical air motions. The SL is considered 

statically unstable if the motions increase in intensity with height and stable if they are 

suppressed to some degree. 

As wind turbine rotors have increased in size and height, their rotors have exceeded the 

maximum height of the SL and now reach into the mixed or residual layer (ML or RL). The 

depth of the ML can vary from a few hundred meters to as much as 2 km above ground level. 

Most important is that the turbulence characteristics of the ML can be quite different from those 

in the SL. In addition, the turbulence scaling relationships of the ML are not as well understood 

as those in the lower SL. The turbulence models currently used in the turbine design standards 

used for type certification are based on SL scaling and characteristics. As a result, they do not 

always adequately reflect the wind and turbulence characteristics that occur in the ML. 

2.2 Turbulent Energy Production and Scaling

To understand how atmospheric turbulence—or perhaps the kinetic energy contained within 

atmospheric turbulence—induces dynamic responses in a wind turbine as its rotors ingest that 

turbulence or energy, it’s helpful to see what controls the energy level within the turbine inflow. 

A useful device here is to define the components of the turbulent kinetic energy (TKE) budget. 

2.2.1 The TKE Budget

If we assume that the turbulence is relatively homogeneous in the horizontal (at least over 

distances much greater than the turbine rotor disk diameter), neglect large-scale atmospheric 

sinking motions (subsidence), and ignore the effects of moisture, we can use a reduced form of 

the local TKE budget suggested by Panofsky and Dutton (1984) as 

∂ET  ∂u  g ∂  ' wE = − T (u w ' ') + (w T ') − ( ' ) − ε . (2-1) ∂t ∂z T ∂z  

I II III 

19
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Here we define ET as the total TKE present or contained with the volume of the air being 

measured, which we define as 

E = , (2-2) T Eiso + Ecoh 

where Eiso is the isotropic contribution to ET and Ecoh is the coherent portion, given by 

2 2 2 1/2 Ecoh =1/ 2[( uw ' ') + (u v' ') + (vw ' ') ] . (2-3) 

By coherent we mean intermittent patches of turbulence, which have a definite spatial-temporal 

organization, in the flow. We have found that on average the ratio Ecoh / ET tends to be about 

0.4, indicating that most of the time the observed turbulence was not purely isotropic (when Ecoh 

would have been 0). The distinction between ET and Ecoh will become clearer later. The mean 

flow has been aligned with the mean wind direction, so u, v, and w represent the streamwise, 

lateral, and vertical velocity components in an orthogonal right-handed coordinate system. In 

this system, positive u points in the downwind direction, v is positive to the left, and positive w 

follows the direction of positive z. Height is indicated by z positive upward, g is the gravity 

acceleration, ε is the viscous dissipation rate of TKE, and θ is the potential temperature given by 

0.286  po  θ = T (2-4)    p  , 

where T is the air temperature in degrees Kelvin and the reference atmospheric pressure po is 

1,000 if the atmospheric pressure p is in hectopascals (hPa; millibars [mb]). The primed 

quantities represent fluctuating values from which the mean has been removed. 

Equation 2-1 expresses the contributions to the local rate of change in total TKE that a wind 

turbine blade passes through. Term I, a production term that is always positive, is the product of 

the mean vertical flux or transport of horizontal momentum ( u w' ') and the mean vertical shear. 

Term II can be either positive or negative, depending on the sign of mean vertical temperature 

flux (w'θ ') . This is the buoyancy term that, if positive, adds energy to the TKE of the air. If 

negative, the buoyancy term removes energy from the TKE of the air by damping or slowing 

down the motions of the turbulent eddies. Buoyant turbulence production/damping is an 

anisotropic process because it acts only in the vertical (Stull 1988, p. 157). We will see this later 

in the report. The damping action, in particular, plays a significant role in the characteristics of 

the turbulence being generated and the resulting wind turbine rotor aeroelastic response. Term 

III represents the vertical transport of total TKE into and out of the local volume. Later we see 

that the vertical transport of the coherent content of the TKE (w’ Ecoh) can also be very important 

in the dynamic response of wind turbines to turbulence. The quantity ε represents the energy 

loss due to viscous dissipation. 

The vertical transport or fluxes of heat, moisture, and momentum are relatively constant with 

height in the SL. The height of this layer can reach 100 m during the day, but it is much 

shallower at night. Monin and Obukhov (M-O; 1954; as referenced in Kaimal and Finnigan 

20
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[1994]) demonstrated that the turbulence in the SL can be scaled by only a few parameters 

measured at the surface (similarity theory). These include the velocity, temperature, and height 

scaling parameters, where the overbar indicates a temporal mean: 

friction velocity, *o [− u w' ]1/2 u = ( ' ) (2-5) o 

−(w' ' θ ) T* = o (2-6) 

u* 

−u3θ M-O length, LM O− = * , (2-7) kg w( 'θ ') 

where k ≅ 0.4. Equation 2-1 can now be rewritten as 

∂ET 2  ∂u  g ∂ = u*   + ( ' ' − (w ' E T wT ) ) −ε. (2-8) ∂t ∂z T ∂z  

So the local mean rate of change of ET within a turbine rotor disk is the sum of the turbulence 

being generated by the shearing stress, the turbulent buoyancy flux, the transport of externally 

generated ET into the volume, and the energy being lost to viscous dissipation. 

2.2.2 Atmospheric Stability

The vertical distribution of heat, momentum, and moisture has a strong influence on the 

characteristics of PBL turbulence, including the spectral distribution of ET and therefore, by our 

definition, its constituents Eh and Ecoh. A measure of stability that we have found very useful in 

correlating wind turbine aeroelastic responses is the gradient Richardson number, Ri, given by 

( g /θ )(∂θ / ) ∂z

Ri = . (2-9) 

( u z∂ )

2 

∂ / 

The Ri is the ratio of turbulence production/damping produced by buoyancy to that being 

produced by shear. A negative value of Ri (unstable conditions) indicates convective turbulence 

generation conditions. A positive value (stable conditions) indicates that turbulence generation is 

being suppressed. A value of zero is associated with neutral conditions in which turbulence is 

being created solely by shearing stress (vertical wind shear) and buoyancy plays no role. This 

condition is rare in the layers generally occupied by modern wind turbines, at least over a 10­

minute period. For example, during an entire year of data collected at the Lamar Low-Level Jet 

Project (LLLJP) site on the high plains of southeastern Colorado, neutral stability conditions 

measured over heights ranging from 3 to 115 m above the surface were observed only 0.14% of 

the time. 

In the SL under steady conditions, appropriate stability scaling is given by the ratio of the height 

to the M-O length LM-O, or 

21
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

g θ θ

z L/ MO = − , (2-10) 3 / z 

( / )(w' ')o 

− u k * 

where the zero subscript indicates the buoyancy flux is measured at the surface (Kaimal and 

Finnigan 1994). A negative value of z/LM-O indicates unstable conditions; a positive one 

indicates stable conditions. Above the SL, M-O similarity scaling tends to break down, 

particularly in stably stratified nocturnal boundary layers. No universal consensus currently 

exists on how to scale ML turbulence. Today, because of their height, the rotor disks of most 

large wind turbines reside completely within the ML/RL, particularly at night. We believe that 

turbulence scaling that is sufficient for a turbine rotor operating within the SL is inadequate for 

one immersed in partially or entirely within the ML. It has been found that local scaling is often 

useful in the ML (Holtslag and Nieuwstadt 1986). Here locally measured values of the scaling 

parameters u* and z/L are used to scale turbulence frequency spectra and other properties; 

therefore, they are functions of height. 

As we will see when we discuss the turbulence scaling used in TurbSim stochastic inflow 

turbulence code (TurbSim), our approach is a hybrid arrangement that uses both surface-based 

and locally scaled parameters. The amplitude and frequency distributions of the spectral 

distributions of the turbulence wind components in the SL are functions of [u*]o and [z/LM-O]o, 

as found by Kaimal and colleagues (1972). Our hybrid scaling approach uses the turbine layer 

gradient Richardson number (RiTL) as a primary scaling parameter for both the turbulent inflow 

and turbine aeroelastic responses. It is calculated over the height of the vertical layer from near 

the surface (2 to 3 m) to the maximum height of the turbine rotor disk. To properly scale the 

turbulence frequency spectra, then, we needed to find an equivalent value of local z/LM-O from 

RiTL. Businger and coauthors (1971) found the following relationships for the SL over flat, 

homogeneous terrain under steady (equilibrium) conditions: 

/ M O− zL , − ≤ 2 / z L ≤ 0

R i ={ . . (2-11) − ( / M O )(1 + 4.7) 1 z L 0 ≤ z L ≤ 1 − / 

Based on our measurements, we had to modify these relationships for two of the spectral models 

used in TurbSim. We give more detail on these modifications later in the report. 

Finally, we define the flux Richardson number stability parameter (Rif) as 

( g / ( ' T w θ ') v ) (g T/ v )( w'θ ') Ri = = , (2-12) f 

u w ( u z / ) *

2 '' ∂ ∂ u ( ∂ ∂ u / )z 

where Tv is the virtual temperature, defined as the temperature of a parcel of completely dry air 

that would need to have the same density if it contained moisture. The Rif is the ratio of the rate 

of turbulence production by buoyancy to the rate produced by shear (Kaimal and Finnigan 1994). 

22
 
 

 

 

We will see later that Rif is useful in gaining insight into the physics of an atmospheric dynamic 

stability condition of importance to wind turbine operations. 

2.2.3 Identification of Turbulence-Turbine Response Scaling Variables

The parameters in Equations 2-4 through 2-12 that are responsible for the production and 

transport (fluxes) of TKE or ET and its constituents are a useful source of independent variables 

with which to correlate or scale the dynamic or aeroelastic response of wind turbine components 

to turbulent conditions. Turbulence variables are separated into mean and fluctuating (zero 

mean) parts such as u = u u + ' . In addition to height and time, we make particular use of the 

following turbulence (primed) variables or combinations and the vertical gradients of these 

variables (such as Ri) as predictors of turbine aeroelastic response: 

•	 u’,v’,w’ (or equivalently ui’) for the streamwise, lateral, and vertical turbulent
 

(fluctuating) wind velocity components
 

•	 u*, or equivalently u w' '

•	 The Reynolds stress components u’w’, u’v’, and v’w’ 

•	 The potential θ’ and absolute T’ temperatures. 

23
 
 

 

 

 

 

 

 

 

 

3.0 Analyzing Turbulence-Turbine Dynamic Response of Micon 

65/13 Turbines 

In this section we discuss the results of our correlation of the dynamic loads and fatigue damage 

observed on the Micon 65/13 turbines in the California wind farm. Our objective was to identify 

turbulence characterization parameters that showed strong correlations with the turbine structural 

and aeroelastic response and could be used to scale that response. 

3.1 Identifying Turbine Response and Turbulence Scaling Parameters

A major objective of our study was to identify the inflow conditions responsible for significant 

accumulations of fatigue damage in turbine components. Accordingly, measurements of dynamic 

loads formed the basis of the turbine response variables. We used the measured loads data from 

the available 397 records and applied load cycle-counting using the Downing-Socie rainflow 

algorithm (Downing and Socie 1982). This gave us distributions of alternating bending moment 

loads or stress cycles (Mp-p). We found that these loading spectral distributions were of the 

mixed type and could be fitted as the sum of a Gaussian distribution for the frequent, lowamplitude stress cycles and (with the exception of the edgewise root bending stress) as a 

decaying exponential distribution for the less frequent higher amplitude stresses. This is 

schematically diagrammed in Figure 3-1. We then fitted individual exponential distributions of 

Ncyc for each of the available data records and found the corresponding slopes, β1. This is 

schematically diagrammed in Figure 3-2 and given by 

−β M − Ncyc = β0e 1 pp 

. (3-1) 

As an example of a turbine of a different design, Figure 3-3 pictures an observed exponential 

alternating root bending load distribution measured by the National Renewable Energy 

Laboratory (NREL) on a two-bladed, downwind AWT-26 turbine installed in the Tehachapi Pass 

area of Southern California. 

Figure 3-4 shows an example of the characteristic shape of a root edgewise cyclic load spectrum 

measured by NREL on a similar but modified Micon 65/13 (called a Micon 65/13M) turbine 

operated at a Great Plains site near Bushland, Texas. Again, the entire load spectrum can be 

expressed as a mixed distribution. The decaying high-cycle, low-amplitude peak at the left is 

24
 
 

Figure 3-1. Schematic of relationship of high-frequency, low-amplitude Gaussian stress cycle 

distributions with lower frequency, high-amplitude exponentially distributed stress cycles 

Figure 3-2. Schematic showing definition of exponential fit to high-amplitude, low-frequency tail of 

alternating stress cycle distribution 

25 
 

 

well approximated by a Gaussian distribution. We found that the more important (from a fatigue 

perspective) second peak could be accurately fit with a Type I extreme value distribution where 

this peak corresponds to the cyclic loading induced by gravity and is given by 

   M     M   

pp 1 p p  1 Ncyc   0 exp exp     1 , (3-2)

     2   2  

where γ2 is the shape parameter that quantifies the high-loading slope portion of the rightmost 

peak distribution shown in Figure 3-4. 

Figure 3-3. Example of root flapwise root bending spectrum from AWT-26 turbine installed in
 

Tehachapi Pass, California 

26 
 

 

 

 

 

 

Source: Sutherland and Mandell (2004) 

Figure 3-4. Examples of two aggregated record periods of 111.5 and 19.3 hours of root edgewise 

cyclic load spectra from modified Micon 65/13 “M” turbine installed in Bushland, Texas, for mean 

wind speeds in 11- to 13-m s–1 range. The peak near 20 kNm is the cyclic load induced by gravity. 

The greatest fatigue damage occurs in the high-amplitude tail, particularly for the composite 

materials used in wind turbine blades (see Veers [1983] and Sutherland [1994, 1999]). We 

hypothesized that the slopes of the high-amplitude tails, as described by the exponential and 

extreme value distribution shape parameters β1 and γ2 in Figures 3-2 and 3-4, are proportional to 

the cumulative fatigue damage. A sharp downward slope indicates fewer large stress cycles and 

less fatigue damage, whereas a shallow slope is related to a greater number of higher amplitude 

loading cycles and greater fatigue damage. 

Our preliminary analysis of the behavior of these slopes indicated that the rates of change were 

strongly related to the character of the inflow turbulence. To establish such a connection, we 

applied stepwise multiple-linear regression analysis techniques and analysis of variance 

(ANOVA). Next we identified the turbulence scaling parameters that were the most efficient in 

predicting the slopes of the high-amplitude loading cycles of the available turbine dynamic 

parameters. To accomplish this, we stratified the population of 10-minute records from the two 

Micon 65/13 turbines into three stability (RiTL) and six hub mean wind speed categories. 

Unfortunately meteorological scaling variables are often inherently cross-correlated to varying 

degrees. This results in significant colinearity in the multiple-regression modeling results and can 

mask the true relationships. The purpose of turbulence similarity scaling discussed earlier was to 

identify a set of independent scaling parameters for the surface layer (SL). Monin and Obukhov 

(1954) found that the u*, the T*, the M-O length LM-O, and the height above the ground z 

27
 
 

 

 

 

 

 

 

 

 

 

 

satisfied the independence requirement for turbulent flows that are in equilibrium (both 

mechanically and thermally) with the underlying surface. 

We cross-correlated the following inflow turbulence characteristic parameters with values of the 

β1 and γ2 load spectral shape parameters: 

• The mean hub-height horizontal wind speed,U H 

• Standard deviation, σ H

• Turbulence intensity, σ H /U H 

• Wind direction standard deviation, σ WD

• The local (hub-height) and turbine layer friction velocities and u*o u respectively *hub 

• The three mean turbulence Reynolds stresses, uw ' ', uv ' , and ' vw ' '

• The turbine layer vertical stabilities Ri and z/LM-O. 

We used a stepwise regression process to correlate groups of turbulence parameter predictors 

with the response variables β1 and β2. The process was continued until the remaining predictors 

converged to a maximum value of the coefficient of multiple regression R2 at the 95% 

confidence level. 

The results from both turbines were combined here. In general, the values were higher (better 

correlations) for the turbine with the NREL rotor because it was more dynamically active and 

was better matched to the range of wind speeds available. More details are given in Kelley 

(1993), but Table 3-1 summarizes the results. It is clear from these results that the temporal 

correlation of the turbulent velocity component covariances (mean Reynolds stress components) 

can exert a significant influence on the high-amplitude loading events via the β1 and γ2 scaling 

parameters. Figure 3-5 plots the variation of both the flapwise and edgewise load shape 

parameters with the hub-height value of u* and the turbine layer value of RiTL. These plots 

indicate that the large loading peak occurs not during neutral stability (adiabatic or RiTL = 0) 

conditions but when the stability of the flow resides within a narrow and weakly stable range; 

i.e., +0.01 < RiTL < +0.05. This means that diabatic flow conditions must be considered when 

simulating the turbulent inflows needed to drive the dynamic design codes. Considering these 

conditions allows us to reproduce the loading conditions seen over the important narrow and 

weakly stable RiTL range indicated in Figure 3-5. 

28
 
 

Table 3-1. Correlation of Loading Distribution Model Shape Parameters with Turbulence Parameter 

Predictors
 

Turbine Dynamic Statistical Model Scaling Parameter β1 

Dominant Inflow Coefficient of 

Predictor(s) Multiple Regression 

R2 

Root flapwise Exponential 1/2 0.71 =   bending moment u uw' ' * 

−( ) hub 

Low-speed shaft Exponential 1/ 2 

' '   0.61 

torque * ( ) hub u uw = 

−  , Ri 

Low-speed shaft Exponential 1/2 0.88 =   bending u uw' ' * 

−( ) hub 

Yaw-drive torque Exponential ( ) ( ) 1/ 2 1/ 2 

u w u v Ri ' ' , ' ' , 0.76 

Tower-top torque Exponential )

1/2 0.77 U H , (uw ' '

Tower axial bending Exponential 0.61 

Tower in-plane Exponential 1/2 0.67 

σ H

U H , u v'' bending ( )

Nacelle axial thrust Exponential ( ) ( ) 1/ 2 1/ 2 

uw uv ' ' , ' ' 0.26 

Nacelle in-plane Exponential 1/2 0.59 , u v'' thrust U H ( )

Tower axial thrust Exponential ( )

1/ 2 

u w Ri ' ' , 0.38 

Tower in-plane thrust Exponential 1/2 1/2 1/2 0.48 (uw uv ' ') , ( ' ') , (vw ' ')

Scaling Parameter γ2 

Root edgewise Extreme Value 1/2 1/2 0.74 

uw ' ' , ' ' v w bending moment ( ) ( )

Source: Kelley (1993) 

29
 
 

(a) 

(b) 

Figure 3-5. Variation of blade root load (a) flapwise (1) and (b) edgewise (2) shape parameters 

with hub-height u* and RiTL 

30 
 

 

 

 

 

 

 

 

 

 

3.2 Measuring Fatigue Damage

Sutherland and Kelley (1995) analyzed the flapwise root loads data collected from the two 

Micon 65/13 turbines. They computed the fatigue damage using Miner’s rule for a GP 0/45 

laminate material and based on the measured cyclic root flapwise load spectra from each of the 

blades. The results confirmed our hypothesis that the bulk of the damage occurs from the 

relatively infrequent, high-amplitude load cycles (100 cycles/h or less, that is, the exponentially 

decaying tail in the lower right of Figures 3-1, 3-2, and 3-3). The greater numbers of large load 

cycles in these tails also translate to a smaller or shallower slope β1 in the exponential 

distribution. This is the condition that occurs in the narrow stability range shown in Figure 3-5, 

which would suggest that high fatigue damage occurs under such conditions. Sutherland and 

Kelley also found that most of the fatigue damage occurs in the 11- to 13-m s–1 hub-height mean 

wind speed range. This range includes the rated wind speed for the turbine equipped with the 

NREL rotor. The resulting fatigue damage for the available observations was almost identical for 

both turbines. 

3.3 Using Stochastic Turbulence Inflow Simulation

In 1992 Kelley expanded the original stochastic inflow turbulence simulator SNLWIND 

developed by Veers (1988; see also Kelley [1992]). He used the measurements collected in 1989 

from the two 50-m met towers upwind and downwind of the California wind farm. Using these 

data and Veers’ single wind component adiabatic simulation as the computational kernel, he 

developed a diabatic simulation of the vector wind (three wind components: streamwise, u; 

cross-wind or lateral, v; and vertical, w). Kelley developed site-specific spectral distributions and 

spatial/temporal coherence models over the observed range of atmospheric stabilities, producing 

a simulation model called SNLWIND-3D. Along with much of the original SNLWIND, Kelley’s 

work forms the basis of TurbSim. What has been called the “Sandia Method” of the original 

SNLWIND code continues to provide the computational kernel of TurbSim. In 1996, Kelley, in 

support of the collaboration with Sandia National Laboratories (SNL), added a spectral model 

simulation to the SNLWIND-3D code to simulate conditions at Row 37. He used the 1990 data 

taken from the met tower upwind of the two Micon 65/13 turbines to provide local scaling. The 

spectral models available in the SNLWIND-3D code were identified as Upwind or Row 1, Row 

37 (7 D row-to-row turbine spacing), and Downwind (14 D spacing to nearest upwind operating 

turbines). Spectral models specified by the International Energy Commission (IEC) Kaimal and 

von Kârmân Normal Turbulence Models (NTMs; IEC 2005; IEC 1999) were also later 

incorporated. 

Kelley and Sutherland (1996) compared the fatigue calculated from long-term simulations using 

SNLWIND-3D. The simulations included a full diurnal cycle with varying boundary conditions 

at Rows 1 and 41 of the California wind farm and an 8-hour simulation of with constant 

boundary conditions at Row 37. The inflow simulations were used to drive an aeroelastic model 

of the Micon 65/13 using the generalized, multibody dynamics code ADAMS (now 

MSC.ADAMS). The simulated results were compared with 2.3 hours of measured data from 

the Micon 65/13 with the NREL rotor. The fatigue damage calculated from the simulations was 

considerably less than that calculated from the measurements using Miner’s Rule. Examining the 

predicted and observed load spectra revealed that the simulations lacked the few but very largeamplitude cycles that were present in the observed data. The lack of those large-amplitude cycles 

31
 
 

 

 

Figure 3-6. Comparison of measured and simulated Micon 65/13 turbine with NREL rotor root 

flapwise load distributions at Row 37 in California wind farm 

had resulted in a slope β1 that was steeper (less damaging) than that observed for the 8-hour 

simulation shown in Figure 3-6. We concluded that something was missing from the SNLWIND3D inflow simulations and that missing element was responsible for the discrepancy. Other 

comparisons with measured data from other turbines pointed to the same situation. 

3.4 Further Quantifying Micon 65/13 Turbine Dynamic Response to Turbulence 

Scaling Parameters

The TurbSim simulations must reproduce the turbulence characteristics that have a significant 

influence on turbine dynamic response. Correlations using the slope of the high-loading tail of 

the load spectra with a range of turbulence scaling parameters showed that only a few turbulence 

scaling parameters were efficient predictors for the responses of the turbine components listed in 

Table 3-1. Results from MSC.ADAMS simulations of the Micon 65/13 turbine with the NREL 

rotor using the Row 37 (7 D) spectral model in SNLWIND-3D showed good agreement with 

observations in the body of the load distributions. These results failed, however, to predict the 

few large load cycles that were responsible for the majority of the measured fatigue damage. To 

gain a more detailed understanding of what conditions are likely to produce these large loads, we 

32
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

repeated the multiple-linear correlation analysis using the same turbulence predictor variables, 

but this time we used fatigue damage equivalent loads (DELs) as the response variable. The DEL 

has become the wind industry standard for assessing fatigue damage. The fatigue DEL is given 

by 

∑(Li ) Ni 

1/ m m 

 i  DEL = , (3-3)   No    

where Ni is the number of loads of magnitude Li, No is 2,000, and m is the Wöehler exponent. 

An m value of 10 for is typically used for composite materials, and a value of 3 is used for steel. 

DEL is the value of the cyclic load amplitude that would create the equivalent amount of fatigue 

damage as the spectrum of loads Li that was measured or simulated. 

Sutherland (2002) and Nelson and coauthors (2003) statistically analyzed the response of the 

previously mentioned modified Micon 65/13M in Figure 3-4 that was operated with a natural 

upwind fetch at the Great Plains site near Bushland, Texas. This Micon turbine had been 

modified to operate at 55 rpm and incorporated a commercial version of the NREL 7.9-m blade 

used on the California wind farm turbine. With the higher rpm, the turbine rated power was 

increased from 65 to 115 kW. These investigators used many of the turbulent flow parameters 

that we used in correlating the slope of load spectra from the two turbines in the California wind 

farm, except they used the blade root flap bending moment (FBM) DEL as the response variable. 

In his analysis, Sutherland found a dependency on Ri that decreased with increasing mean wind 

speed, but observed that the DEL was also sensitive to the standard deviations of the lateral (v) 

and particularly the vertical (w) turbulence components. Similar to what we found from the San 

Gorgonio data, Sutherland showed that at higher wind speeds the sensitivity to the local friction 

velocity u* became predominant and that Ri plays an important role overall. 

Nelson and colleagues (2003) applied sophisticated numerical techniques to the same data set to 

isolate the turbulence parameters from their interdependencies as much as possible, to establish 

specific levels of sensitivity to the turbine response. They identified mean wind speed and the 

wind speed standard deviation as the primary inflow variables contributing to the turbine 

dynamic response. They also applied their numerical technique to the residuals after accounting 

for the two primary variables by using many of the same turbulence scaling or predictor 

variables as Kelley (1993) and Sutherland (2002). They concluded that none of these secondary 

turbulence predictors contributed significantly to the response beyond the primary variables of 

mean wind speed and wind speed standard deviation. 

The turbulent inflow to the modified Bushland Micon 65/13M turbine was significantly different 

from that entering the rotors of the California wind farm turbines on Row 37 ̧ where 36 rows of 

turbines were operating upwind with the closest row 7 D upstream. The large-scale atmospheric 

dynamics that influenced the turbulence characteristics at the inflow of each of these turbines 

were also much different. At the California wind farm, the two 50-m towers yielded data 

suggesting that a high-speed flow stream (jet) forms above the wind farm at night in response to 

33
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

the increased drag and warmer temperatures in the layer the wind turbines occupy near the 

ground (similar to nocturnal flows over forest canopies). 

We found evidence that during the night this jet-like structure periodically becomes dynamically 

unstable and creates a strong downward flux of organized turbulence into the turbines below. 

The natural fetch upstream of the turbine at Bushland was flat and relatively homogeneous 

agricultural land whose surface roughness varies with the growing stage of the crops in the 

upwind fetch. This area is frequently under the influence of nocturnal LLJs during the warmer 

months. These streams of higher speed air create downward fluxes of organized turbulence two 

or three times per night when instabilities develop in the stratified layers beneath the jet 

maximum velocity. 

How often LLJs occur at Bushland is unknown. Without directly comparing the turbulence 

statistics and corresponding turbine responses from the turbines on Row 37 of the California 

wind farm and the one on the Bushland site, it is impossible to quantify any differences arising 

from location, which is further complicated by the modified configuration of the Bushland 

Micon 65/13M test turbine. 

Based on Sutherland’s findings of the sensitivity of the blade root FBM DELs to the RiTL and the 

hub-height u*, we believe these parameters deserve more attention in establishing a broader 

perspective of the role of turbulence in the dynamic response of wind turbines. The California 

wind farm test turbines operated in the aggregated wake conditions created by 36 rows of 

upstream turbines, the closest of which was seven rotor diameters. It was much more energetic 

and organized than the natural inflow at the Bushland Micon 65/13M turbine. If anything, we 

believe that the observed sensitivities to the various turbulence parameters would be more 

pronounced in the response of the turbines at Row 37 in the wind farm because there is “more 

signal,” meaning increased turbulence levels, to drive the turbine response dynamics. 

3.5 Defining the Role of Coherent Turbulent Structures in Micon 65/13 Dynamic 

Response

Our comparisons of simulated loads with observed loads showed that we were missing the 

largest ones. To understand if the turbulence characteristics of the simulated inflow were 

somehow deficient, we examined a number of detailed records from the Micon turbines in which 

we synchronized the time series of load variables with turbulence parameters. Figure 3-7 

illustrates a typical case in which there were several large load cycles observed with the 

corresponding Reynolds stress and associated local vorticity components. Figure 3-7b shows a 

coherent turbulent structure embedded in the flow between about 3.5 and 6.5 seconds, as 

indicated by the large cross correlations in the instantaneous u’v’(t) and v’w’(t) Reynolds stress 

components. We estimated the local vorticity components over a period of 1 second from the 16­

per-second velocity components measured by the ultrasonic anemometer. The relative helicity 

indicated by H in the diagram is a measure of the intensity of the spin associated with this 

turbulent structure. In addition to the spin, this structure was coherent because it had a definite 

temporal as well as a likely spatial organization because both turbines responded to its presence, 

though not in the same way. The NREL rotor primarily responded in the root edgewise bending 

load, and all three of the blades of the AeroStar rotor responded in the flapwise bending 

direction. 

34
 
 

 

 

 

 

 

 

 

 

 

 

 

 

3.5.1 An Application of Wavelet Analysis

To understand the role of coherent turbulent structures in inducing strong aeroelastic response in 

wind turbine rotors, we developed a capability to analyze this interaction with time-frequency 

analysis tools and specifically wavelets (see Kelley et al. [2000] for more details). Wavelet 

analysis allows one to examine both the frequency and temporal distribution of energy associated 

with transient events. Figure 3-8 presents a continuous wavelet transform decompositions 

(scalograms) of the three Reynolds stress components (shown in the top panel) of a measured 

turbulent inflow to the Micon 65/13 with the NREL rotor and the resulting root flapwise load 

response. Time is plotted on the abscissa and the cyclic frequency on each of the ordinate axes, 

with the nonlinear frequency scales inverted. The deep red represents the highest intensity of the 

variable and the darkest blue the lowest. Coherent patches, such as those at about 5 seconds in 

the record, show intense levels of kinetic energy in all three Reynolds stress components 

(covariances) that cover a wide frequency range. The flapwise bending load shows significant 

levels of high frequency energy between about 14 and 20 seconds, probably caused by the 

intense coherent structure identified by the Reynolds stress components. 

We used the Row 37 spectral model in SNLWIND-3D to simulate higher wind speed flows that 

may produce the extreme loading events seen at the California wind farm. Figure 3-9 shows the 

time series of the hub-height wind speed, Reynolds stress components, and flapwise bending 

load with the mean removed. Although no discrete or sharp edge gusts in the wind speed are 

present, two coherent structures are indicated by the Reynolds stress components. The one in the 

center of the record is the more intense and it has a significant flapwise loading response. 

The continuous wavelet transform decomposition shows intense levels of strain energy reaching 

frequencies greater than 5 Hz in the peaks. The lowest panel displays seven frequency bands 

from the discrete wavelet transform of the time series of the flapwise loading. The amplitude of 

the time series shown in the frequency bands indicates the intensity of the load within the band. 

The frequency ranges of the bands are 0.125–0.25, 0.25–0.5, 0.5–1.0, 1.0–2.0, 2–4, 4–8, and 8– 

16 Hz for the B7, B6, B5, B4, B3, B2, and B1 bands, respectively. Figure 3-10 shows the details 

of continuous wavelet decomposition of the three Reynolds stress components and their 

relationship to the transient flapwise bending load response. These diagrams demonstrate that the 

turbine responds with an organized or coherent loading response when an organized or coherent 

turbulent structure is ingested by the rotor and is likely a major contributor to the large, 

infrequent loading cycles seen in the tails of the stress distributions. Such a process can 

simultaneously drive several lightly damped vibrational modes in turbine structural components, 

which in turn can contribute by constructive interference (in-phase summation or addition) to 

produce the large load excursions clearly demonstrated in Figures 3-8, 3-9, and 3-10. 

35
 
Figure 3-7. Significant loads seen on Micon 65/13 NREL and AeroStar rotors: (a) load excursions 

in flapwise and edgewise root loads; (b) corresponding instantaneous u’v’ and v’w’ Reynolds 

stresses and estimated local vorticity components ωy and ωz. H is the local relative helicity, a 

measure of the intensity of the spin in the structure. A coherent turbulent structure exists in the 

flow between about 3 and 6.5 seconds to which the turbine rotors responded. 

36 
Figure 3-8. Continuous wavelet decomposition of inflow turbulence Reynolds stress components 

and root flapwise bending load of NREL-rotor-equipped Micon 65/13 turbine 

37 
Figure 3-9. Continuous and discrete wavelet decomposition of Micon 65/13 turbine blade root 

flapwise bending response to SNLWIND-3D simulated inflow containing embedded coherent 

structure. The uppermost panel is the time series of the hub-height wind speed, the second panel 

contains the time series of the three Reynolds stress components, the third panel is the flapwise 

bending load with the mean removed, the fourth panel is the continuous wavelet transform 

decomposition of the flapwise bending load, and the bottom panel is the discrete transform 

decomposition into seven frequency bands, with B7 the lowest frequency (0.125–0.25 Hz) and B1 

the highest (8–16 Hz). 

38 
Figure 3-10. Continuous wavelet decompositions (scalograms) of simulated individual Reynolds 

stress components of coherent turbulent structure and corresponding response of Micon 65/13 

turbine root flapwise bending load 

39 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.5.2 Defining a Variable That Represents the Level of Coherent Turbulent Energy 

in the Flow 

The DEL parameter gives us with a single number that represents the level of fatigue damage 

that has occurred in a data record. Other useful response variables would be the second statistical 

moments or extreme values. Using wavelet analysis, we demonstrated that the intensity of the 

Reynolds stresses in the flow have a significant influence on the level of dynamic response in 

turbine components such as the blades in addition to stability expressed as 

2 2 2 1/2 E coh =1/ 2[( uw ' ') + (uv ' ') + ( ' vw ') ] . (3-4) 

This definition of Ecoh allows us to include the influence of coherent turbulence with other 

predictor variables on the level of turbine component dynamic response expressed by a single 

quantity such as the DEL, standard deviation, or extreme value. For example, Figure 3-11a plots 

the population variation of the three-blade average DEL of the root FBM for the NREL rotor 

equipped Micon 65/13 against the hub-height maximum or peak value of Ecoh More information 

is gained, however, from the smoothed contour plot of Figure 3-11b, where the FBM DEL values 

are plotted against both the peak value of Ecoh and RiTL. 

3.5.3 Statistical and Contour Analysis

Our approach to establishing the turbulence characteristic parameters that have the most 

influence on the scaling of the turbine dynamic response variables has been to use both multiple 

linear and stepwise regression and graphic presentations. The graphics are presented as bivariate 

scatterplots with and without smoothing and smoothed 3-D contour plots similar to those in 

Figure 3-11b. For the contour plotting we employed locally weighted linear regression, or 

LOESS (see Cleveland and Devlin [1988] for more information), for generating the smoothed 

contours. The LOESS algorithm is very useful for smoothing complex 3-D scatterplots that may 

contain complex underlying deterministic structures. No fitting function is required a priori, only 

a smoothing parameter that ranges from 0 to 1. For a highly populated raw scatterplot, we used 

0.5 for most contour smoothing. For those that had fewer points, it was sometimes necessary to 

increase the value from 0.7 to 0.9. It was also necessary to detect and remove any outliers before 

applying the LOESS algorithm because of the local nature of the process, and the presence of 

outliers could introduce artifacts into the smoothed subsets of points. 

3.5.4 Expansion of Candidate Turbulence Parameter Predictors

With the knowledge that coherent turbulence plays a role in the dynamic response of wind 

turbines, we expanded the list of candidate turbulence parameter predictors beyond those 

originally used to correlate with the slope of the load distributions or spectrums and whose 

results are listed in Table 3-1. We calculated the correlation matrix from the entire San Gorgonio 

data from Row 37 for these parameters as predictor or independent variables and four response 

variables. The response variables were the three-bladed average DELs and the peak of the DELs 

from the individual blades for the root FBM of each turbine. In Table 3-2 we summarize the 

turbulence parameters and their correlation coefficients that exceeded 0.3. Coefficients that 

exceed 0.7 are shown in red and those exceeding 0.5 are italicized in bold black. Two 

independent variables have not been previously defined, the buoyancy frequency, Nbuoy and the 

standard deviation of the vertical flux or transport of coherent turbulent kinetic energy, σ . w E' coh 

The former is also referred to as the Brunt-Väisälä or buoyancy frequency given by 

40
 
 

 

 

 

 

g d θ N = (3-5) buoy θ dz 

where θ is the potential temperature. Nbuoy is the frequency at which a vertically displaced parcel 

of air will oscillate in a statically stable atmosphere. It is related to Ri as 

2 2 Ri = ( g /θ )(∂θ / ∂z) / (∂U / ∂z)

2 

= Nbuoy / (∂U / ∂z) . (3-6) 

We find that the mean wind speed (either the horizontal or streamwise component) and their 

standard deviations are highly correlated, as did Nelson and coauthors (2003). Sutherland (2002) 

found that the Bushland data correlated well with Ri and u*hub as well as parameters involving 

the vertical wind component w. We find the same in Row 37 in San Gorgonio along with several 

additional parameters tabulated in Table 3-2. Clearly parameters in this table that involve the 

second statistical moments of all three of the velocity components (kinetic energy) are highly 

correlated with the blade fatigue loads. We shall shortly see why the variation of the vertical 

transport of ' coh " wE “makes the list.” It is interesting to note the relatively low correlation with 

stability (RiTL) and the standard deviation of the vertical wind component w in this bivariate 

analysis. We shall see shortly that these low correlations are somewhat misleading in this format. 

41
 
 

 

FBM DEL (kNm) 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

10 

(a) 

20 

Hub Peak Ecoh (m2s-2) 

30 40 50 60 70 

60 (b) 

50 

-2) Hub Peak 

Ecoh (m2s 

40 kNm 

20 

30 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

-0.3 -0.2 -0.1 0.0 0.1 0.2 

RiTL 

Figure 3-11. Variation of NREL-rotor-equipped Micon 65/13 three-blade peak root FBM DEL with (a) 

hub peak Ecoh only and (b) RiTL and hub peak Ecoh. Negative values of RiTL indicate dynamically 

unstable, zero neutral, and positive stable flow conditions. 

42 
 

 

 

 

 

 

 

 

Table 3-2. Cross-Correlation Coefficients for Inflow Turbulence Parameters with FBM DELs 

for Values > 0.3 

NREL AeroStar NREL AeroStar 

Rotor Rotor Rotor Rotor 

3-Blade 3-Blade 3-Blade 3-Blade 

Average Average Peak Peak 

DEL DEL DEL DEL 

U Hhub 0.871 0.845 0.808 0.823 

σ UH 0.742 0.720 0.684 0.697 

Ri TL 0.371 0.359 0.328 0.338 

u 0.602 0.596 0.551 0.581 *o 

u 0.698 0.674 0.650 0.672 *hub 

Nbuoy 0.349 0.341 0.311 0.311 

Hub peak Ecoh 0.539 0.523 0.495 0.480 

σ w E' 0.639 0.631 0.606 0.613 coh 

U 0.868 0.842 0.804 0.820 

σ u 0.749 0.725 0.692 0.704 

σ v 0.518 0.487 0.508 0.483 

σ w 0.365 0.375 0.349 0.361 

E T 0.751 0.728 0.711 0.710 

σ u w' ' 0.725 0.719 0.673 0.693 

σ u v' ' 0.669 0.670 0.664 

σ v w' ' 0.566 0.549 0.550 0.542 

0.704 

43
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.6 Identifying Micon 65/13 Turbulence Scaling Sensitivities

It is apparent from Table 3-2 that the fatigue damage at the blade roots of the two Micon turbines 

is influenced by more than the mean wind speed and its standard deviation. Figure 3-12 shows a 

plot of the variation of the root FBM DEL with mean wind speed. Although the strong 

correlation with mean wind speed is obvious, several large loads deviate from the power law 

trend, particularly at greater than rated wind speed (12.5 m s–1) on the Micon turbine with the 

NREL rotor. In Figure 3-5a we show that the slope of the large loading tail varied with the 

stability expressed as RiTL and the hub-height local shearing stress or friction velocity u*. In 

Figure 3-13a, we plot the variation of the three-blade averaged FBM DELs for the NREL and 

AeroStar rotors that has been minimally smoothed by LOESS local regression with a very small 

overlap (smoothing parameter). This allows smaller peak variations to be identified, albeit with 

somewhat less certainty. Figure 3-5a is repeated as Figure 3-13b for ease of comparison. We see 

that large levels of DELs occur, and a greater number of large loading cycles (shallow or smaller 

value of β1) occur over the same weakly stable and narrow RiTL range of about +0.01 to +0.025 

and with higher values of the local value of u*. For comparison, Figure 3-14 presents a LOESSsmoothed contour plot of the variation of the FBM DELs from the NREL-rotor equipped Micon 

turbine with RiTL and u*; this is similar information as in Figures 3-5a and 3-13b but with fatigue 

damage as the response variable. Even though the sensitivity of fatigue loading does not register 

as being that significant in Table 3-2, it is clear from Figures 3-13 and 3-14 that the stability as 

expressed by RiTL does play a central role in turbine dynamic response. 

3.6.1 Turbine Dynamic Response Sensitivity to Turbulent Velocity Characteristics

The relationships between the various turbulence scaling parameters in Table 3-2 are best 

understood with a series of 3-D contour plots using the Richardson number as the independent 

variable. Using the entire available data set, Figures 3-15a and b show the relationships between 

the FBM DELs and the largest load value in a 10-minute record as functions of RiTL, hub u*, and 

the hub peak value of Ecoh . The heaver solid and dashed vertical lines correspond to the RiTL 

range (0 to +0.05) in Figure 3-13a, where the most fatigue damage takes place from the 

definitions of β1 and γ2, which were confirmed by Sutherland and Kelley (1995). The vertical 

dash-dot-dotted line (0.025) is the value of RiTL when the loads are the most sensitive to the peak 

Ecoh and to a somewhat lesser extent to the hub value of u*. Figures 3-15c and d compare the 

sensitivities of the largest FBM loads with these same three parameters. Here the greater 

response associated with the larger and lighter NREL rotor and is particularly sensitive to the 

hub-height peak Ecoh within the 0 to +0.05 RiTL range. 

Figure 3-16 plots the sensitivity of the three-blade average FBM DELs with stability and the 

standard deviations of the three hub-height turbulence components, σu, σv, and σw. Here the 

response characteristics are similar for both rotors, but the NREL rotor is a bit more sensitive. 

The sudden increase in fatigue loads to the turbulence energy in all three of the components as 

the flow becomes stable is dramatic. Both rotors are very sensitive to σw beginning at RiTL = 

+0.01 and extending to about +0.05. The dashed lines indicate a σv/σu ratio of 0.8, which is the 

value specified to scale the crosswind or v-component turbulence in the IEC Kaimal NTM (IEC 

2005, Table B-1). The σw/σu ratio used to scale the vertical turbulence component is 0.5, which 

is less than the minimum value shown on the plots in Figure 3-17. These plots indicate that high 

44
 
Root FBM DEL (kNm) 

24
 NREL rotor
 

AeroStar rotor
 

22
 NREL rotor rated wind speed
 

AeroStar rotor rated wind speed
 

20
 

18
 

16
 

14
 

12
 

10
 

8
 

5 6 7 8 9 10 15
 

Hub mean wind speed, UH (ms-1)
 

Figure 3-12. Variation of blade root FBM DELs for NREL and AeroStar rotors with hub-height mean 

wind speed for all available records

45
3-blade averaged FBM DEL (kNm) 

13 

14 

15 

16 

17 

18 

19 

NREL rotor 

AeroStar rotor 

(a) 

-0.10 -0.05 0.00 0.05 0.10 

RiTL 

(b) 

Figure 3-13. Comparison of variation of (a) three-blade averaged FBM DEL and (b) slope (β1) of 

high-loading tail with RiTL. The dashed lines in (a) delineate a critical or sensitive stability range 

for loads with the dot-dot-dashed line representing the most sensitive Ri value. 

46 
Hub local u * (ms -1 ) 

1.6 

1.8 

2.0 

2.2 

2.4 

2.6 

2.8 

8 

10 

12 

14 

16 

FBM DEL 

(kNm) 

-0.3 -0.2 -0.1 0.0 0.1 0.2 

RiTL 

Figure 3-14. LOESS-smoothed contours of variation of FBM DELs from NREL-rotor-equipped 

Micon 65/13 turbine with RiTL and hub-height local u* value. Dashed and dot-dot-dashed lines 

correspond to those of Figure 3-13a delineating a critical stability range for loads. 

47 
 

NREL Rotor

RiTL

u*

hub (m/s)

AeroStar Rotor

- l

RiTL

Hub Peak Ecoh (m2/s2

)

l 

Ri

u

* hub (m/s)

l i

RiTL

Hub Peak Ecoh (m2/s2

)

NREL rotor AeroStar rotor
 

0.2 

0.4 

0.6 

0.8 

1.0 

1.2 

1.4 

1.6 

1.8 

8 

10 

12 

14 

16 

18 

20 

3 b ade 

Average 

FBM 

DEL 

(kNm) 

u *hub (ms-1 )

(a) 

-0.3 -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2

20 

30 

40 

50 

60 

8 

10 

12 

14 

16 

3-b ade 

Average 

FBM 

DEL 

(kNm) 

Hub peak E coh (m2s -2 )

(b) 

-0.3 -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2

0.2 

0.4 

0.6 

0.8 

1.0 

1.2 

1.4 

1.6 

1.8 

8 

12 

16 

20 

24 

28 

Largest

F apw se BM 

(kNm) 

60 

u *hub (ms-1 ) 

(c) 

-0.3 -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2 

Hub peak 

Ecoh (m2

s-2) 50 

40 

30 

20 

-0.3 -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2 

RiTL 

Figure 3-15. Variation of FBM loads: (a) three-blade average DELs vs. RiTL and hub u*; (b) threeblade average DELs vs. RiTL and hub peak Ecoh; (c) largest FBM value vs. RiTL and hub u*; (d) 

largest FBM value vs. RiTL and hub peak Ecoh 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

Largest 

Flapwise BM 

(kNm) 

(d) 

48 
 

 

U V W 

4.0 2.8 

3.5 

3.5 2.6 

3.0 3.0 2.4 3-Blade 

Average

2.2 FBM DEL 2.5 2.5 

m/s 

(kNm) 

NREL 

Rotor 

2.0 

2.0 2.0 6 

1.8 7 

8 1.5 1.5 9 

10 -0.3 -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2 11 

1.6 

4.0 12 2.8 

13 3.5 

3.5 14 2.6 15 

3.0 16 3.0 2.4 17 AeroStar 

2.5 2.5 

18 2.2 Rotor m/s 

19

2.0 

2.0 2.0 

1.8 

1.5 1.5 1.6 

-0.3 -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2 

RiTL Ri Ri TL TL 

Figure 3-16. Variation of three-blade averaged FBM DELs with RiTL and standard deviations of 

hub-height turbulence components σu , σv , and σw 

V U W /U W / V 

1.5 2.0 

1.4 1.8 

1.8 

1.3 1.6 1.6 1.2 

1.4 1.4 3-Blade 

Average 

m/s m/s 

NREL 1.1 FBM DEL 1.2 1.2 1.0 (kNm) 

0.9 1.0 6 

7 

1.0 

0.8 0.8 8 0.8 9 0.7 0.6 10 

-0.3 -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2 11 

12 1.5 2.0 13 

1.8 14 1.4 1.8 15 

1.3 16 1.6 1.6 17 

1.2 18 1.4 1.4 19 1.1 

Rotor 

AeroStar 

Rotor 

1.0 1.2 1.2 

0.9 1.0 1.0 

0.8 0.8 0.8 

0.7 0.6 

-0.3 -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2 

RiTL RiTL RiTL 

Figure 3-17. Variation of three-blade averaged FBM DELs with RiTL and ratios of σv /σu, σw /σu, 

and σw /σv . The dashed line of 0.8 on the σv/σu plots indicates the scaling used in the IEC Kaimal 

NTM. 

49 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

fatigue loads in this critical stability region are clearly related to the greater turbulent energies in 

the crosswind and vertical directions as compared with the streamwise direction. This 

characteristic is not simulated in the neutral IEC Kaimal NTM. 

Figure 3-18 further underscores the sensitivity of this critical stability range. Here we show the 

variation of the peak FBM loads with stability and the three mean Reynolds stress components. 

We previously was that the turbine loading is a strong function of the vertical momentum flux 

uw ' ' when it is expressed as the local u* value, but the highest peak loads are also associated 

over a wide range of magnitudes of the uv ' ' and vw ' ' components as well in this weakly stable 

regime. The highest load peaks occur with large values of these cross correlations, which can be 

interpreted as lateral fluxes of turbulent energy that are most likely are associated with the strong 

coherent turbulent motions and turbulent mixing occurring in this narrow stability range. It is 

within this range that the highest wind speeds are available, as is shown in Figure 3-19. 

A primary scaling parameter for the IEC Kaimal NTM is the hub-height turbulence intensity, 

Ihub. Turbine loads are expected to increase with Ihub. For the two Micon turbines at Row 37 in 

the California wind farm, we found the opposite for the FBM peak loads, as plotted in Figure 3­

20. In the left column of this figure the greatest peak loads on both rotors, although taking place 

within with the narrow stability range discussed previously, occur at the lowest turbulence 

intensities. For comparison, the variation in the peak FBM loads with hub-height peak Ecoh is 

plotted in the right column, showing a strong positive correlation with the peak response, again 

within this narrow stability range. 

3.6.2 Turbine Dynamic Response Sensitivity to Atmospheric Thermodynamics

The turbulence dynamics associated with this weakly stable stability range have a strong thermal 

component, as seen in Figure 3-21. Here we have plotted the variation of three-blade average 

FBM DELs for the Micon equipped with the NREL rotor with the standard deviation of the hubheight temperature σ T in Figure 3-21a and the temperature (buoyancy) flux wT ' ' in Figure 3­

21b. The highest DELs are associated with large variations in temperature and buoyancy flux in 

more stable conditions (RiTL > 0.05), but significant fatigue damage does occur in the narrow +0 

to +0.05 range with lower values of σ T and wT ' ' . Similarly, the peak FBM loads on each 

turbine are strong correlated with the calculated mean buoyancy flux in the proper units, as 

shown in Figure 3-22, particularly in the critical Ri range. None of this occurs in a neutral 

atmosphere because the buoyancy forces do not exist. 

Other turbine components are also affected by conditions within this critical stability range. For 

example, Figure 3-23 plots the variation of the peak low-speed shaft bending loads with stability 

and the vw ' ' covariance. Figure 3-24 shows the sensitivity of the peak low-speed bending loads 

with the hub local u* and peak Ecoh for both rotors. The loading associated with this critical 

stability range filters down through the entire turbine structure, as demonstrated in Figure 3-25. 

Here the variation of the peak axial thrust developed by the NREL rotor is correlated with the 

hub-height local u* and the peak Ecoh. The largest thrust forces in the downwind direction (+X) 

are generated within the critical stability range and are quite sensitive to high values of u* and 

Ecoh. By contrast, the largest upwind (–X) thrust forces occur during unstable flow conditions. 

50
 
 

RiTL

28 

NREL Rotor AeroStar Rotor 

-3.5 

-3.0 

kNm 

8 

12 

16 

20 

-2.5 

-2.0 24 

-0.3 -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2 

2 -2 2 -2 m s 

m -1.5 uw ' '

u v' '

vw ' '

-1.0 

-0.5 

0.0 

-3 

-2 kNm 

8 

-1 12 

16 

20 

-0.3 -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2 

24 

2 

0

-2 s 1 

2 

3 

0.8 

0.6 

kNm 

0.4 8 

12 

16 0.2 20 

24 

0.0 

m 

-0.3 -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2 

s -0.2 

-0.4 

-0.6 

-0.8 

Figure 3-18. Variation of peak FBM loads with RiTL and hub-height mean Reynolds stresses 

51 
U hub (ms-1) 

16 

14 

12 

10 

8 

6 

4 

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 

RiTL 

Figure 3-19. Variation of hub-height mean horizontal wind speed with RiTL. The critical RiTL range 

is shown between +0.01 and +0.05 (dashed lines). 

52 
 

NREL Rotor Hub Peak E coh (m 2 /s 2 ) 

-0.3 -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2 

60 

0.35 

50 

0.30 

40 

30 

I hub I hub 

0.25 

0.20 20 

AeroStar Rotor 

-0.3 -0.2 -0.1 0.0 0.1 0.2 

Hub Peak 

Ecoh (m 2 /s 2 ) 

4 

8 

12 

16 

20 

24 

Largest 

Flapwise BM 

(kNm) 

60 

0.35 

50 

-0.3 -0.2 -0.1 0.0 0.1 0.2 

RiTL 

0.30 

40 

0.25 

30 

0.20 20 

RiTL 

Figure 3-20. Variation of peak FBM loads with RiTL, hub-height turbulence intensity, Ihub, and peak 

Ecoh 

53 
 

(b) (a) 

T ( oK) 

5.0 

4.5 

4.0 

3.5 

3.0 

2.5 

2.0 

1.5 

RiTL 

-0.3 -0.2 -0.1 0.0 0.1 0.2 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

3-blade 

Average

FBM 

DEL 

(kNm) 

RiTL 

-0.3 -0.2 -0.1 0.0 0.1 0.2 

w'T' (o K-ms-1 ) 

2 

4 

6 

8 

10 

12 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

3-blade 

Average 

FBM 

DEL 

(kNm) 

Figure 3-21. Variation of Micon 65/13 turbine with NREL rotor three-blade average FBM DEL with 

hub-height (a) σT and (b) buoyancy flux, wT ' '

54 
 

 

NREL Rotor Aerostar Rotor 

(g/Thub )(w'T') (m2 s -3 ) 0.05 

0.10 

0.15 

0.20 

0.25 

0.30 

0.35 

4 

8 

12 

16 

20 

24 

28 

Peak 

FBM 

(kNm) 

-0.3 -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2 

RiTL 

Figure 3-22. Variation of peak FBM loads with stability and mean buoyancy flux 

Figure 3-23. Variation of peak low-speed shaft bending loads with RiTL and the hub-height vw ' '

Reynolds stress component 

55 
 

 

(b) (a) 

NREL rotor Peak Low-Speed Shaft Bening Load (kNm) AeroStar rotor Peak Low-Speed Shaft Bending Load (kNm) 

Hub Peak 

Ecoh (m 2 /s2) Hub u * (m/s)

1.8 1.8 

1.6 1.6 

1.4 1.4 

1.2 1.2 

1.0 1.0 

0.8 0.8 

0.6 0.6 

0.4 0.4 

0.2 0.2 

60 60 

50 50

40 40

30 30

20 20

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

-0.3 -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2 

RiTL 

Figure 3-24. Variation of peak low-speed shaft bending loads with stability and hub u* and Ecoh 

56 
 

NREL rotor Peak Axial (+X) Nacelle Thrust Force (kN) 

1.8 

1.6 

1.4 

1.2 

1.0 

0.8 

0.6 

0.4 

0.2 

24 

22 

20 

18 

16 

14 

12 

26 

28 

14 

14 

22 

24 

12 

28 

26 

10 

NREL rotor Peak Axial (-X) Nacelle Thrust Force (kN) 

1.8 

1.6 

1.4 

1.2 

1.0 

0.8 

0.6 

0.4 

0.2 

-6 

-6 

-8 

-8 

-6 

-6 

-6 

-6 

-6 

-12 -10 -8

-8 

-14 

-16 

-10 

-18 

-12 

Hub Peak Ecoh (m2/s2) Hub u * (m/s) 

60 

50 

40 

30 

20 

20 18 

16 

14 

12 

22 

24 

12 

10 

16 14 

10 

12 

16 

18 

60 

50 

40 

30 

20 

-8 

-8 

-6 

-6 

-4 

-10 -8 -6 -12 

-14 

-16 

-18 

-0.3 -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2 

RiTL 

Figure 3-25. Variation of nacelle axial thrust force (kN) on Micon 65/13 turbine equipped with NREL 

rotor with hub-height u* and peak Ecoh 

57 
 

 

 

 

 

 

 

 

 

 

3.7 Flow Details of Critical Stability Range

Our previous results showed that the greatest turbine dynamic response and fatigue damage 

measured on the two Micon turbine rotors do not occur in neutrally stable boundary layer 

conditions. They do, however, take place within the narrow and weakly stable RiTL stability 

parameter range of +0.01 to +0.05, with maximum turbine dynamic responses at a value near 

+0.02. We believe it is useful to look at the details of the flow conditions associated with this 

stability range to understand why it is responsible for the fatigue damage seen in these two 

particular turbine rotors and operating environment and whether or not it is unique. 

3.7.1 Role of Vertical Turbulence Transport

In Figure 3-26 we plot some of important flow details associated with this critical stability range. 

Figure 3-26a plots the hub-height mean momentum ( uw ' ') and buoyancy fluxes ( wT ' ') for the 

entire available data set. The locally measured downward momentum flux increases dramatically 

just as the flow becomes stable (RiTL > 0) and reaches a peak value at an RiTL of +0.02 (indicated 

by the dot-dot-dashed vertical line). The buoyancy flux increases under the same change in 

stability, except when RiTL reaches +0.02 it rapidly decreases. Above this value of RiTL, both 

fluxes decrease with increasing stability with rate of decrease in uw ' 'larger than in the 

buoyancy. We believe we are seeing the effects of negative buoyancy damping becoming 

dominant when the layer RiTL reaches +0.02. Between 0 and +0.02 are large, intense organized 

structures in the flow whose motions are not being significantly constrained by the limited 

damping in this stability range. As the stability and negative damping increase, an expanding 

number of oscillatory modes that form in the slightly stable flow are attenuated, this in turn 

reduces the turbulent energy in the corresponding turbulent eddy scales. 

In addition to the locally evolving flow characteristics, Figure 3-26b shows the strong positive 

(upward) and negative (downward) transports (fluxes) of coherent TKE (Ecoh) taking place 

within this critical stability range. The high surface temperatures are responsible for the positive 

fluxes of Ecoh that are scaled on the left-hand ordinate. The downward flux into the rotor disk 

layer of Ecoh (scaled on the right-hand ordinate) is, however, much greater. We know from the 

measurements taken from the taller 50-m towers the year before that under stable conditions a 

flow of higher speed air (jet) forms over the wind park. Turbulent momentum is then transferred 

downward toward the ground and into the wind farm from this higher speed air, which includes 

coherent turbulence structures, as indicated by Figures 3-26a and b. These conditions produce a 

very unsteady flow that is manifested by the high degree of variation in level of Ecoh indicated by 

the plot of σ Ecoh shown in Figure 3-26c. This variance reaches a peak in the RiTL range of 0 to 

+0.02 and decreases with increasing stability. 

58
 
12 0 

10 -1 

8 

w'T' (

oK-ms-1)

-2 

-2) u'w' (m2s 

6 

-3 

4 

-4 

2 

w'T'
 

u'w'
 (a) -5

0 

-0.2 -0.1 0.0 0.1 0.2 

400 RiTL 400 

300 

200 

200 

100 0 

0 -200 

-100 -400 

-200 

(b) -600 

-300 

-0.2 -0.1 0.0 0.1 0.2 

RiTL 

5 

-3) Negative Peak w' Ecoh (m3s 

s-3) Positive Peak w' Ecoh (m3 

-2) (m2

s  

Ecoh

4 

3 

2 

-0.2 

Ecoh 



-0.1 

RiTL 

0.0 0.1 0.2 

(c) 

Figure 3-26. Details of variation of fluxes in critical stability range: (a) w T' '

and uw ' '; (b) positive and negative w E' coh values; and (c)  Ecoh 

59 
 

 

 

 

 

 

 

 

3.7.2 The Role of the Diurnal Variation and the Dynamics of the Critical Stability 

Range

Figure 3-27 plots the diurnal variation of some of the key parameters that influence the FBM 

DELs on the two Micon 65/13 turbines. One of the characteristics of the California wind farm is 

the low wind speeds (frequently below turbine cut-in) between about 1000 to 1500 LST because 

of the larger scale atmospheric dynamics. The highest wind speeds typically occur about 3–4 

hours after local sunset, or between 2100 and 2400 LST, which also happens to be when a 

significant number of the turbine outages occurred. As the figure shows, the RiTL is very close to 

+0.02 a significant amount of the time between about 1900 to 2300 LST, which is also when the 

largest fatigue loads tend to occur. The figure shows that the greatest FBM DEL values occurred 

on both turbines at 2000 hours. Concurrent with these elevated loads, the RiTL was near +0.02, 

the hub u* and peak Ecoh values were very high, and there were intense downward fluxes of 

coherent TKE ( ' ) of more than –500 m3 s

–3 w E . The period between midnight and about 0300 coh 

hours experienced some significant loads, and some records showed the stability within this 

narrow critical range and downward Ecoh fluxes reaching as large as −400 m3 s

–3 . 

60
 
San Gorgonio Row 37 Wind Farm Micon 65s 

16

14 

sunrise sunset 

-1 

12 

ms

10 

8 

6 NREL rotor rated 

4 

Hub U wind speed 

0.2 

0.1 

0.0 

-0.1 RiTL = +0.02 

-0.2 RiTL Ri TL= +0.05 

60 

50 

s -2

40 

m 2 

30 

20 

10 Hub Peak Hub peak CTKE 

2.0 

-100 

1.6 

-200 

3 s -3

-300 1.2 

m-400 0.8 

-600 

-500 Hub Peak negative 

w' Ecoh 

Hub u* 

(ms-1) 0.4 

20 

18 

16 

kNm 14 

12 

10 

6 

8 3-blade average DEL 

NREL rotor 

AeroStar rotor 

0 3 6 9 12 15 18 21 24 

Local standard time (h) 

Figure 3-27. Observed diurnal variations of Uhub, RiTL, hub u* and peak Ecoh, negative peak w’Ecoh, 

and three-blade average FBM DELs for Micon 65/13 NREL and AeroStar rotors. Each data point 

represents the values from an individual 10-minute record. 

61 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4.0 Analyzing Turbulence-Turbine Dynamic Response of the 

NWTC ART 

In 1999–2000, we were able to expand our research into examining the role of atmospheric 

turbulence in the dynamic response wind turbines through a measurement program using a 

larger, 600-kW turbine installed in the rigorous wind flow of the National Wind Technology 

Center (NWTC). This experiment was an integral part of the Long-Term Inflow and Structural 

Testing (LIST) Program jointly conducted by the National Renewable Energy Laboratory 

(NREL) and the Sandia National Laboratories (SNL). 

The results from the Micon 65/13 turbine testing deep within the California wind farm showed 

that the greatest fatigue damage typically occurred within a weakly stable diabatic flow within 

the atmospheric layer occupied by the turbines. The level of damage was also sensitive to the 

local turbulent shearing stress or friction velocity u*, the variation in the vertical velocity 

expressed as its standard deviation, and the turbulent vertical flux or transport of coherent 

turbulent energy. In 2002, SNL found similar sensitivities using a modified version of the Micon 

65/13 turbine and an upwind planar array at a Great Plains site near Bushland, Texas. 

The California wind farm experiment demonstrated the role of organized or coherent turbulent 

structures in creating significant dynamic loads in the turbine structural components. The NWTC 

LIST experiment allowed us to measure the turbine dynamic response to an energetic but natural 

turbulent inflow and then compare that with what was found in deep within the California wind 

farm. Further, the upwind planar array provided us with measurements of variation of the inflow 

turbulence characteristics both vertically and laterally across the dimensions of the turbine rotor 

disk. 

In this section we present an overview the results of the measurements on the Advanced 

Research Turbine (ART) turbine similar to those from the Micon 65/13 turbines, i.e., the 

sensitivities to the turbulence characteristics found important in the California wind farm. We 

also use the much larger (1,569 LIST records versus 397 for the Micons) measurement database 

to more fully explain and validate some of the processes identified earlier and their relationships 

to turbine response and the atmospheric conditions that produce it. Finally, we present direct 

comparisons between the turbulence-induced dynamic responses observed on the San Gorgonio 

Micon turbines and the NWTC ART to demonstrate the underlying similarities for two 

significantly different inflow environments. 

4.1 ART Dynamic Response to NWTC Inflow Turbulence Characteristics

The variations of the out-of-plane (flapwise) root bending damage equivalent load (DEL) with 

the hub peak Ecoh and mean wind speed are shown in Figures 4-1a and b, respectively. Figure 4­

1a shows that the DEL varies as a power law with Ecoh. Figures 4-2 and 4-3 present expanded 

versions of these plots, including, in addition to the flap bending moment (FBM) DELs, the 

maximum alternating load cycle, the peak FBM, and the peak with the mean load removed for 

the entire available population and the observed with the mean below-rated wind speed . Two 

attributes stand out. First, Figure 4-3 shows greater scatter about the trend line in plots of the 

response variables to the mean wind speed as compared with the variation with Ecoh in Figure 4­

2. Second, Figure 4-2 clearly shows a significant number high load responses (a positively 

62
 
Blade Out-of-Plane BM DEL (kNm) Blade Out-of-plane BM DEL (kNm) 

250 

300 

350 

Significant 

Moderate 

Threshold 

Response Characteristic (a) 

200 

150 

100 

50 

0 

Hub peak Ecoh (m2s-2) 

1 10 100 

300 

350 

rated wind speed (b) 

250 

200 

150 

100 

50 

Hub mean wind speed (ms-1) 

2 4 6 8 10 12 14 

0 

16 18 

Figure 4-1. Variations of NWTC ART root bending moment DEL with 

hub-height (a) peak Ecoh and (b) mean wind speed 

63 
Figure 4-2. Variations of FBM with hub-height peak Ecoh: (1) DELs, (2) maximum 

alternating (rainflow) cycle, (3) peak value, and (4) peak value with mean removed for 

entire available population (left column) and below-rated wind speed (right column) 

64 
 

Figure 4-3. Same as Figure 4-2, except with variation with hub-height mean wind speed 

65 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

skewed distribution) across almost the entire wind speed range, particularly in below-rated wind 

speed conditions in the right column. 

Our analysis of the level of the FBM dynamic response with hub peak values of Ecoh indicated a 

threshold of about 2 m2 s

–2, a moderate response at 5 m2 s–2, and a significant response at 10 m2 

s

–2 or more. These threshold criteria have been annotated on Figure 4-4a, which is further 

substantiated by the box plot distributions in Figure 4-4b. This significant response threshold is 

further supported by the DEL probabilities shown in Figures 4-1a and Figure 4-2, which show 

definite increases in the DEL values for peak values of Ecoh of 10 m2 

s

–2 or more. 

One characteristic of the turbulent inflow to the NWTC ART is the low value of vertical shear, 

even in stable flow conditions. Figure 4-5a plots the expected values of the power law shear 

exponent α as function of the hub-height mean wind speed for unstable and stable flow 

conditions. Higher than about 11 m s–1 α is expected to remain below the commonly used value 

of 1/7 and the IEC Normal Wind Profile (NWP) value of 0.2 (IEC 2005; Section 6.3.1.2). Figure 

4-5b shows the variation of the FBM DELs, and demonstrates that they are poorly correlated 

except that the lowest fatigue loads occur at high values of α. Figures 4-6a and b plot the 

relationships among α, the mean hub-height wind speed, and RiTL. They also show the critical 

stability range found in the California wind farm (RiTL = +0.01 to +0.05). The figures show that 

the α value generally remains less than the IEC NWP value of 0.2 within the critical stability 

range but are accompanied by high mean wind speeds. 

Figure 4-7b shows the observed variations of the FBM DELs with RiTL. Figures 4-7a and 4-7c 

plot the corresponding variations in the hub peak Ecoh and σw, respectively. The California wind 

farm critical Ri range has also been added to each plot showing the sensitivity of these 

parameters to this weakly stable flow condition. The FBM fatigue response and the 

corresponding turbulence parameters peak Ecoh and σw decrease significantly for RiTL values 

greater than 0.1, as is indicated by the dotted line and indicating an approximate upper stability 

limit for larger loads. In the analysis of the California wind farm turbine fatigue and load 

excursion responses, the hub-height friction velocity u* and RiTL were found to be sensitivity 

parameters, particularly for the former higher wind speeds. In Figure 4-8a we plot the observed 

variation of hub u* with RiTL and indicate the critical stability range. Figure 4-8b plots the 

variation of hub u* with the mean hub-height wind speed. Figure 4-8c shows the approximately 

monotonic variation of the FBM DELs with hub u*. 

4.2 Vertical Inflow Inhomogeneity and Gradients within the ART Rotor Disk

The ART rotor disk is approximately twice the diameter of the California wind farm Micon 

65/13 turbines and projects another 35 m (115 ft) deeper into the planetary boundary layer. We 

used the 23-m (75-ft) hub or 2 m (6 ft) below it (the location of the sonic anemometer) as the 

reference height on the Micons because it was considered reasonably representative of this 

smaller rotor. The ART rotor spanned twice the vertical distance of the Micons, however, and we 

cannot arbitrarily make the same assumption of flow homogeneity across such a large rotor. In 

Figures 4-9a and b, we compare the variations of the FBM DELs with the standard deviations of 

the vertical wind component (σw) and the vertical flux (transport) of coherent turbulent kinetic 

energy (w’Ecoh) with height. Figure 4-9a shows that the observed fatigue damage is very highly 

66
 
350 

(a) 

300
 

250
 

200
 

150
 

100
 

50
 

( Peak Ecoh => 10) 0
 

-1 01 234 5 
 

Probability (%) 

350
 

(b) 

300
 

250
 

200
 

150
 

100
 

50
 

0
 

Peak CTKE <= 10 Peak CTKE > 10
 

-2 (m ) 2

s

Figure 4-4. Confirmation that hub peak Ecoh (CTKE) values greater than 10 m2 s–2 are 

indicative of significant response and resulting DEL: (a) probability distribution of FBM 

DEL with 10 m2

 s–1 threshold shown; (b) box plots of FBM DEL distributions for values of 

peak Ecoh ≤10 and > 10 m2 s–2

Root flap BM DEL (kNm) Root flap BM DEL (kNm) 

67 
 

 

0.30 

(a) RiTL < 0
 

Ri > 0
 TL 0.25 

1/7 shear exponent 

IEC NWP value 

0.20 

0.15 

0.10 

0.05 

0.00 

0 5 10 15 20 25 

Hub (37m) mean wind speed (ms-1) 

350 

(b) 

300 

250 

200 

150 

100 

50 

1/7 shear exponent 

IEC NWP 

0 

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 

rotor 

Figure 4-5 (a) Available population of expected variation of ART rotor disk shear 

exponent α with hub (37-m) mean wind speed for unstable (RiTL < 0) and stable (RiTL > 0) 

flows; (b) variation of FBM DEL with rotor disk α. In general, the FBM DELs are not well 

correlated with α, although the lowest values tend to occur at its highest values. Root FBM DEL (kNm) Expected rotor disk shear exponent 

68 
Rotor 

 Hub 

UH (m/s) 

0.35 

(a) 

0.30 

0.25 

0.20 

0.15 

0.10 

0.05 

-0.3 

0.00 

-0.2 -0.1 0.0 0.1 0.2 0.3 

RiTL 

18 

20 

(b) 

16 

14 

12 

10 

8 

6 

4 

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 

RiTL 

Figure 4-6. Variation of (a) rotor disk shear exponent α and (b) hub-height 

mean wind speed with RiTL. The critical RiTL value range of +0.01 to +0.05 

found in the California wind farm is also shown. The mean wind speeds drop 

significantly above an RiTL value of +0.1. 

69 
(a) 80 

Hub w (ms-1) Flapwise BM DEL (kNm) Hub Peak E coh (m2

s-2) 

60 

40 

20 

0 

-0.3 

300 (b) 

250 

200 

150 

100 

50 

-0.3 

2.0 

(c) 

1.5 

1.0 

0.5 

0.0 

-0.3 

NWTC ART Turbine - Row 4 Natural Flow 

-0.2 -0.1 0.0 0.1 0.2 0.3 

-0.2 -0.1 0.0 0.1 0.2 0.3 

-0.2 -0.1 0.0 0.1 0.2 0.3 

RiTL 

Figure 4-7. Variation of (a) hub-height peak Ecoh, (b) FBM DELs, and (c) hubheight σw with RiTL. The critical RiTL stability range found in the California wind 

farm (+0.01 to +0.05) is shown as dashed lines. 

70 
2.0 

(a) 

1.5 

1.0 

0.5 

0.0 

-0.3 -0.2 

2.0 

(b) 

1.5 

1.0 

0.5 

0.0 

4 6 

350 

(c) 300 

250 

200 

150 

100 

50 

0 

0.0 0.2 

Hub u* (ms-1) Flapwise BM DEL (kNm) Hub u* (ms -1) 

-0.1	 0.0 0.1 0.2 0.3 

RiTL 

8 10 12 14 16 18 20 

Hub mean wind speed (ms-1) 

0.4	 0.6 0.8 1.0 1.2 1.4 1.6 

Hub u* (ms-1) 

Figure 4-8. Observed variation of hub friction velocity u* with (a) RiTL and (b) 

hub mean wind speed. Critical RiTL stability range is shown as red dashed lines 

in (a) and the ART rated wind speed is a black dashed line in (b). The variations 

of the FBM DELs with hub-height u* are plotted in (c). 

71 
300 (a)

Blade root flap DEL (kNm) 250 

200 

150 

58-m 

100 

37-m 

15-m 

50 

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 

σw(z) (ms-1) 

Blade root flap DEL (kNm) 

300 (b)

250 

200 

100 

150 

58-m 

37-m 

15-m

0 

50 

5 10 

σw' Ecoh(z) (m3

s-3) 

15 20 25 30 35 

Figure 4-9. Correlation of blade FBM DELs with height variation of standard 

deviations of (a) vertical wind component σw and (b) vertical flux of coherent 

turbulent kinetic energy, w’Ecoh

72
 

 

 

 

 

 

 

 

 

 

 

 

correlated with variations in vertical velocity at the top of the turbine rotor (58 m or 190 ft) and 

less so at the hub height (37 m or 121 ft) and even less at the bottom (15 m or 49 ft). These large 

variations in the vertical wind also translate into significant fluctuations in the vertical transport 

of Ecoh which can induce high levels of fatigue in the blade roots, as is shown in Figure 4-9b. 

The correlations with the FBM DELs show that they are sensitive to Ecoh vertical transport 

fluctuations in the upper portion of the rotor disk (37- and 58-m heights). The vertical 

inhomogenity is further underscored by Figure 4-10a. Here the FBM DELs are shown to be more 

strongly correlated with peak positive (upward) values of the vertical flux of Ecoh ( ' coh wE ) at 

hub height (37 m) but more correlated with negative (downward) w E' fluxes at the top of rotor coh 

(58 m). Figure 4-10b shows the largest variations in peak w E' take place within the critical coh 

stability range. 

Figure 4-11 examines the heterogeneous flow conditions entering the ART rotor and their 

relationship to the fatigue loading further. Here the variations in the FBM DELs and peak Ecoh 

values correlate with the mean momentum flux uw ' ' at the 15-, 37-, and 58-m heights. The 

observed FBM DELs correlate only over a narrow range of uw ' ' at the 15-m height that is mostly 

negative (downward flux), but small positive fluxes are also observed. The peak values of Ecoh at 

this height are more correlated with the downward mean fluxes. At the 37-m height, we see the 

largest mean fluxes and the fatigue loads are correlated with both positive and negative values, 

with the former being more prevalent. Similarly, the peak Ecoh values at this height tend to occur 

with positive momentum fluxes. The largest fatigue loads are associated with the greatest mean 

momentum fluxes, both negative and positive. Finally, using the 58 m as a reference, the fatigue 

loads are highly correlated with primarily downward momentum fluxes, as are the peak values of 

Ecoh at this height. These graphs emphasize the significant spatial heterogeneity of the turbulent 

flows entering the 42-m layer occupied by the ART rotor disk. They indicate the following: 

•	 A significant downward turbulent flux containing coherent elements is entering the rotor 

disk layer from above. 

•	 Strong vertical mixing is taking place within the disk near hub height, which is
 

contributing to the observed high levels of fatigue damage.
 

•	 The vertical momentum flux is being damped out as it approaches the ground, as seen at 

the lowest elevation of the rotor disk, and probably does not contribute as much to the 

observed fatigue loads as is taking place higher in the rotor disk layer. 

73
 
(a) 300 

150 

58-m 

100 37-m 

15-m 

50 

-600 -400 -200 0 200 400 600 

Peak w'Ecoh(z) (m3s-3) 

600 

(b) 

400 

200 

0 

-200 

-400 

-600 

-0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 

RiTL 

Figure 4-10. (a) Correlation of blade FBM DELs with height variation of peak values of 

vertical flux of coherent turbulent kinetic energy, w’Ecoh; (b) variation of peak value of 

w’Ecoh at the top of the ART rotor (58 m) with RiTL. The California wind farm critical 

stability range is shown between the vertical dashed lines. 

3 -3) Peak 58-

m w' Ecoh (m s Blade root flap DEL ( kNm ) 250 

200 

74 
15m 37m 58m 

Figure 4-11. Relationship of blade root flapwise DELs with height variations in peak Ecoh and mean vertical m

75 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4.3 NWTC ART Turbulence Scaling Sensitivities

We found when analyzing the California wind farm Micon 65/13 turbines that LOESS-smoothed 

3-D contour plots are an excellent tool to visualize the relationships between the key turbulence 

scaling parameters and the turbine aeroelastic and fatigue damage as well as between the 

parameters themselves. 

4.3.1 Turbine Aeroelastic Response to the NWTC Natural Inflow

We now examine both the mean and the dynamic response of key turbine structural elements to 

turbulence characteristics to which the Micon 65/13 turbines were most sensitive. 

4.3.1.1 Mean Blade Root Flapwise and Edgewise Bending Loads 

Figure 4-12 plots the smoothed variations of NWTC ART mean root flapwise and edgewise 

bending loads operating in a natural inflow environment as a function of RiTL in. In Figure 4-12a 

the variation of these mean loads is plotted as contours with RiTL and the hub-height average Ucomponent wind speed with the flapwise load on the left and the edgewise on the right. The rated 

wind speed is indicated by a horizontal dashed line. The upper limit (RiTL = +0.05) of the critical 

stability range identified with the Micon 65/13 turbines is shown as a vertical white dashed line. 

In general, the highest mean flapwise loads occur in the vicinity of the rated wind speed and do 

not become sensitive to the stability until it is reached. Afterward a strong correlation with the 

critical stability range extends up to a RiTL value of about +0.10. A similar correlation is seen for 

the mean edgewise bending loads, with the exception that the peak response occurs just below 

the rated wind speed and in slightly unstable (convective instability) flows (–0.05 < RiTL < 0). 

Figures 4-12b and c show the influence of the critical stability range on the flapwise mean loads 

when coupled with the disk-averaged shear stress (u*) and hub peak values of Ecoh. The 

edgewise loads in contrast are more sensitive to unstable or convective flows. One exception is 

the sensitivity to relative high values of Ecoh for RiTL values greater than about +0.15. We return 

to this later for further discussion. 

4.3.1.2 Turbine Nacelle and Low-Speed Shaft Dynamic Response 

Figure 4-13 summarizes the turbine nacelle response as indicated by the accelerometer triad in 

the inertial measurement unit (IMU) mounted on the forward low-speed shaft support bearing 

(pillow block) correlated with the turbine layer stability and the disk-averaged mean Reynolds 

stresses uw ' ' , uv ' ', and vw ' '. Nacelle accelerations exhibit a strong sensitivity in the critical 

stability range, particularly when high degrees of cross-correlations exist in the fore-aft (X) and 

side-to-side (Y) directions; there is, however, much less sensitivity in the vertical (Z) direction. 

This significant sensitivity to the critical stability range is further underscored by the smoothed 

cross-correlation contours in Figures 4-14 and 4-15. The uppermost row of Figure 4-14 shows 

the variation of the nacelle accelerations with the disk-averaged mean buoyancy flux wT ' ' .

These plots show that nacelle accelerations along all three axes within the critical stability range 

are correlated with positive (upward) buoyancy fluxes and large values can also occur with 

strong negative buoyancy fluxes in unstable flows. The significant sensitivity of the 3-D nacelle 

motions to disk-averaged peak Ecoh and its vertical flux or transport w E' coh pictured in the center 

and lowest rows of Figure 4-14 within the critical stability range is unambiguous. This critical 

range sensitivity is further emphasized in the correlations of the nacelle accelerations with the 

disk-averaged variations in the u, v, and w turbulent wind components expressed by their 

standard deviations σ u , σ v , and σ w in Figure 4-15. Figure 4-16 presents contour plots of the 50% 

76
 
Figure 4-12. Smoothed variations of NWTC ART mean root flapwise (left) and edgewise (right) 

bending moments with RiTL and (a) hub-height U ; (b) disk averaged u * ; and (c) hub-height peak 

Ecoh . The dashed line in (a) represents the rated wind speed, 12.8 m s–1. The vertical white dashed 

line indicates the upper limit of the critical stability range. 

77 
 

 

Figure 4-13. Smoothed variations of NWTC ART IMU forward nacelle accelerations with RiTL and 

mean disk-averaged turbulent Reynolds stress components u w' ' , u v' ' , and v w' ' . The variation 

of the fore-aft acceleration ( X ) is shown in the left column, the side-to-side or lateral acceleration 

(Y) in the center column, and the vertical acceleration ( Z) in the right column. 

78 
Figure 4-14. Smoothed variations of NWTC ART IMU forward nacelle X, Y, and Z acceleration 

responses (mg or g/1000) with RiTL and disk-averaged buoyancy flux w T' ' in the top row, peak 

Ecoh in the center row, and Ecoh vertical flux, w E' in the bottom row coh

79 
Figure 4-15. Smoothed variations of NWTC ART IMU forward nacelle X, Y, and Z mean 

acceleration responses (mg) with RiTL and disk-averaged standard deviations of u-component 

( u ) in top row, v-component (  v ) in center row, and w-component (  w ) in bottom row 

80 
 

Figure 4-16. Smoothed variations of NWTC ART nacelle IMU peak longitudinal (±X) [columns (a) 

and (b)] and positive vertical (+Z) [column (c)] peak acceleration responses (g) with RiTL and hub 

height: U (top row); peak Ecoh (center row); and local shear stress or friction velocity u* (bottom 

row) 

81 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LOESS-smoothed variations of the peak positive (downwind) and negative (upwind) 

longitudinal (±X) and positive (upward) (+Z) accelerations with RiTL and the hub-height U in 

the top row, peak Ecoh in the center row, and the mean shearing stress or friction velocity u* in 

the bottom row. It is clear that the largest nacelle accelerations along all three axes are most 

sensitive to weakly convective or unstable flow conditions (RiTL ≅ –0.05). They are also, 

however, the most sensitive to peaks in the hub-height values of Ecoh and u* within the critical 

stability range (+0.01 ≤ RiTL < +0.05), which indicates the presence of coherent turbulent 

motions of the right dimensions in the flow. Similar sensitivities are found in the nacelle peak 

pitch, roll, and yaw angular responses with the hub-height mean wind speed U in Figure 4-17. 

The significant sensitivity of the angular responses to peak values of Ecoh in flows whose 

stability is within the critical stability range is shown in Figure 4-18, again indicating a response 

to the presence of turbulent coherent structures. Finally, Figure 4-19 shows the smoothed 

response of the low-speed shaft torque (τ) variations ( στ ) to variations in stability and the disk 

averages of the Reynolds stress components and turbulent wind component standard deviations. 

Although there is some identifiable sensitivity with stability and the critical range in particular, 

the correlations in variations of low-speed torque are dominated by both the cross-axis turbulent 

wind correlations and variations in the 3-D wind vector. 

4.3.1.3 Turbine Blade Root Flapwise Fatigue Response 

We previously found in the California wind farm Micon 65/13 turbines that low-cycle, high 

amplitude loads and consequently the DELs scaled with the hub-height mean shearing stress or 

friction velocity u* and RiTL. We also found that the DELs were highly correlated with the hubheight peak values of Ecoh. In Figure 4-20 we plot the observed variation of the ART blade root 

FBM DELs with RiTL and disk-averaged u* and peak values of Ecoh. Again we show the upper 

limit of RiTL of +0.05 as a white vertical dashed line. In Figure 4-21 we plot the smoothed 

variation of the FBM DELs with RiTL and the hub-height turbulence intensity ( σ U /U ). Finally, 

in Figure 4-22, we display the variation of the largest observed FBM within an individual 10­

minute record with the corresponding values of RiTL and the disk-average u*. Clearly the critical 

stability range and these two choices of the other turbulence scaling parameters significantly 

influence the level of fatigue damage and peak loads observed for the ART in the NWTC 

operating environment. 

In Figure 4-23 we plot the smoothed variation of the FBM DELs with RiTL and the disk-averaged 

mean Reynolds stress components uw ' ' , uv ' ', and vw ' ', and the buoyancy flux wT ' ' . Again, 

the RiTL range is a significant feature of the response with these variables averaged over the 

entire rotor disk. Because the ART rotor is twice the dimensions of the Micon turbines and 

because it extended deeper into the planetary boundary layer (PBL), we analyzed the variations 

in Figure 4-24 at the three measurement heights of 15, 37, and 58 m available in the upwind 

planar array. The 37-m variables are the means of the three measurements at this height. Figure 

4-24 shows these results for the same scaling variables as Figure 4-23 in columns [a], [b], [c], 

and [d], respectively. Although the general patterns agree with those derived from disk averages 

in Figure 4-23, a closer examination reveals distinct differences in the contours of the DELs with 

some of the scaling parameters with height. For example, the DELs with uw ' ' in column [a]

vary with height with the largest DEL values 

82
 
 

(a) (b) 

Figure 4-17. Smoothed variations of NWTC ART nacelle IMU peak angular response rates (positive 

in column [a] and negative in column b) with RiTL and hub-height mean wind speed U with pitch 

angle response (top row), roll angle response (center row), and yaw angle response (bottom row). 

Horizontal dashed line indicates rated wind speed. 

83 
 

(a) (b) 

Figure 4-18. Smoothed variations of NWTC ART nacelle IMU peak angular response rates (positive 

in column [a] and negative in column [b]) with RiTL and hub-height peak Ecoh with pitch angle 

response (top row), roll angle response (center row), and yaw angle response (bottom row) 

84 
 

 

(a) (b) (c) 

Figure 4-19. Smoothed variations of NWTC ART low-speed shaft torque standard deviation  

(kNm) with RiTL and disk-averaged mean Reynolds stresses u w' ' , uv ' ' , and v w' ' in upper row and 

standard deviations of streamwise (u), lateral (v), and vertical (w) turbulent wind components in 

lower row 

85 
(a) 

(b) 

Figure 4-20. Smoothed NWTC ART variation of root FBM DEL with RiTL and disk-averaged (a) local 

friction velocity u* and (b) peak Ecoh. Upper limit of critical stability range is shown with vertical 

dashed line. 

86 
 

Figure 4-21. Smoothed NWTC ART variation of root FBM DEL with RiTL and hub-height turbulence 

intensity (Ihub) 

87 
Figure 4-22. Smoothed variation of NWTC ART largest flapwise bending load with RiTL and diskaveraged local shearing stress or friction velocity u* 

88 
 

Figure 4-23. Smoothed variations of NWTC ART FBM DELs with disk-averaged (a) u w' ' , (b) uv ' ' , (c) 

v w' ' , and (d) w T' '

89 
 

 

Figure 4-24. Smoothed variations with height of NWTC ART FBM DELs with RiTL and (a) u w' ' , (b) 

u v' ' , (c) v w' ' , and (d) wT ' '

90 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

occurring in the critical stability range at the 58-m height. Also, these large DEL values take 

place in slightly more stable conditions as the height becomes closer to ground. The variations of 

the DEL with the buoyancy in column [d] follow a similar pattern. All of this points to the 

presence of significant heterogeneity in not only the 3-D velocity field but the thermal one as 

well in the naturally occurring flow into the ART rotor disk, which will need to be included to 

achieve a faithful and representative simulation of such conditions. 

4.4 ART Dynamic Response and Inflow Statistical Characteristics

Between October 30, 1999 and May 15, 2000 there are 1,568 records in which we have turbine 

response data that are time synchronized with inflow turbulence data from the upwind planar 

array. We stratified these data into five categories based on RiTL. In analyzing the California 

wind farm data and the response of the Micon 65/13 turbines, we found there were at least four 

and possibly five ranges of RiTL where the turbine response differed. Initially we defined five 

stability ranges or classes (STC or STability Class) defined as STC01 (–1 ≤ RiTL), STC02 (–1 < 

RiTL ≤ 0), STC03 (0 < RiTL < +0.10), STC04 (+0.10 ≤ RiTL < +0.25), and STC05 ( +0.25 ≤ RiTL 

< +1.0). As discussed previously, we found that class STC03 could be further subdivided into 

what we called the critical Richardson number range or CRR as defined by +0.01 < RiTL < 

+0.05, with the maximum turbine response taking place near RiTL = +0.02. Here we define the 

remaining interval +0.05 ≤ RiTL < +0.10 as CRR High or CRRH. Class STC01 contains very 

unstable (auto convective) conditions, STC02 ranges from moderate instability to neutral, STC03 

and its subdivisions of CRR and CRRH are weakly stable with CRR being the weakest, STC04 

is moderately stable, and STC05 is very stable. Our total available inflow data set for the LIST 

Program contains 7,041 10-minute records or a total of 1,174 hours, of which 261 h (1,568 

records) have corresponding time-synchronized turbine response data. We often collected 

meteorological data when the turbine was not available or conditions would not allow it to run. It 

is the analysis of this much larger data set, which we discuss later, that forms the basis for the 

development of the NWTC Spectral Model in the TurbSim Code using the full ranges of classes 

STC02, STC03, STC04, and STC05. 

The LIST data set had no records collected within the most unstable classification STC01 and 

only 16 in the most stable class STC05. Of the available population having the turbine and 

inflow synchronized information available, 98% of it occurred with RiTL values between –0.25 

and +0.25. For the analysis that follows, we ignored the STC05 category because it contained 

such few records. We examined the effect of using the slightly smaller combined range of the 

CRR and CRRH classes with STC03 and found it to be insignificant. The STC02, CRR, CRRH, 

and STC04 classes contained 1,470 10-minute records or 95% those available. The pie chart of 

Figure 4-25 diagrammatically describes the relative sizes of the amount of data available in each 

of the stability classes. Therefore the CRR classification contains about twice as many records as 

the records contained in flows that are neutral to moderately unstable (STC02) and those that are 

slightly more stable (CRRH). 

91
 
Figure 4-25. Available NWTC ART response and inflow turbulence data by stability class 

92 
 

 

 

 

 

 

 

 

 

 

 

4.4.1 Relationship of ART Load and Turbulence Parameter Probability 

Distributions by Stability Classification

In the leftmost vertical panel of Figure 4-26 we display the observed probability distributions in 

boxplot format of three turbine response variables related to the flapwise blade root bending 

moments (FBM) for the STC02, CRR, CRRH, and STC04. In this boxplot format, the outliers 

(less than P10 and greater than P90) are shown as black dots and the means and medians are 

indicated by red and black horizontal lines, respectively, within the quartile shaded box. In the 

center and right panels we plot the corresponding probability distributions for a range of inflow 

turbulence parameters and turbulence scaling parameters that we have found or have been shown 

to influence turbine loading response. 

Examining the blade root responses in the leftmost panel of Figure 4-26, we see that the largest 

loads are associated with the CRR stability class followed by STC02, CRRH, and STC04 in 

descending order. We also see that the hub-height mean U-component wind speed, the diskaveraged local u* or shear stress, and rotor disk peak Ecoh values follow this same pattern as 

shown in Figures 4-26d, e, and g and are consistent with Figures 4-20 and 4-22. The higher 

response of the FBM variables in the CRR stability class is associated with small positive values 

of the flux Richardson number Rif and significant levels of the disk-averaged values of the 

vertical flux of Ecoh ( w E' ) shown in Figures 4-26f and h. Very small positive values of Rif are coh 

indicative of intense vertical turbulent mixing. This is an important clue to understanding the 

atmospheric dynamics associated with this stability class and is discussed in more detail in a later 

section. Finally, Figure 4-26i shows the influence of mean vertical wind shear on each of the 

stability regimes. 

Figure 4-27 plots the corresponding distributions of the peak Reynolds stress components as 

measured at the top of the ART rotor (58 m). We chose the 58-m level as a height because it is 

located within the lower half of the larger wind turbine rotors now installed at the NWTC site 

and in wind farms around the world. Again we point out that the greatest peaks in the CRR and 

STC02 classes in the u v' ' component in Figure 4-27b reach levels almost twice those of the 

other two stress components, indicating the presence of very heterogeneous, non-Gaussian 

conditions in the lateral directions of the inflow. Lastly, the influence of the greater stability of 

the CRRH and STC04 classes is readily apparent on both the body of the distributions and peak 

excursions. 

In Figure 4-28, we examine the statistical characteristics of the buoyancy fluxes within each of 

the four stability classes. Following the format of Figure 4-27, we present the distributions of the 

peak buoyancy fluxes at the top of the ART rotor. Here the largest positive fluxes are associated 

with the unstable class STC02 because of the convection occurring under such conditions. Still, 

however, positive (upward) peaks almost as large are seen in the CRR class distribution. Of 

particular importance is the larger downward peak fluxes seen in the body of the CRR class 

distribution, with similar but smaller distributions in the more stable CRRH and STC04 

distributions. The reason for this is apparent in the distributions shown in Figure 4-28b. Here we 

plot the mean buoyancy flux distributions measured at the top and bottom of the ART rotor (58 

and 15 m, respectively) for each stability class. Although some small differences exist with 

height, such as the slightly larger ranges of variation at the 58-m level, the influence of the stable 

flow conditions relative to the unstable STC02 class is the most obvious and a major player in 

influencing the turbulence characteristics and subsequent impact on the turbine response. 

93
 
Figure 4-26. Probability distributions of both ART dynamic response and range of inflow turbulence parameter

Turbine response variables: (a) root FBM DELs, (b) largest FBM load cycle, and (c) peak FBM load. Inflow parame

(e) disk-average local u*, (f) rotor layer Rif, (g) rotor disk peak Ecoh, (h) rotor disk-average wE ' coh , and (i) rotor disk 

α. 

94 
' ' ' ' 

greater values associated with the u v' ' component, particularly for the CRR stability class, and significant dec

stable CRRH and much more stable STC04 classes. Also note the separations in the mean and medians for the ST

classes that indicate the presence of strong, heterogeneous (non-Gaussian) conditions. 

Figure 4-27. Probability distributions of 58-m height peak Reynolds stress components (a) u w , (b) u v , and (c) 

95 
Figure 4-28. Probability distributions by stability class of (a) peak buoyancy flux ( wT ' ' ) at top of 

ART rotor (58 m) and (b) mean buoyancy fluxes at top and bottom of turbine rotor (15 m) where 

dots represent P05 and P95 quantiles 

96 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4.4.2 Diurnal Variations in NWTC Natural Inflow Characteristics and Observed 

ART Load Extremes 

We found that the diurnal variation of the wind resource within the California wind farm had a 

significant influence on the loads seen on the Micon 65/13 turbines. Typically the hub wind 

speeds there were below or just near cut-in between about 1000 and 1500 LST during the period 

of the observations at the peak of the local wind season. Figure 4-29 plots the probability 

distributions of the diurnal variation in the 50-m mean wind speed from the NWTC M-2 met 

tower for the observational period of the LIST experiment from October 1999 through mid-May 

2000. The cut-in wind speed for the NWTC ART is about 6 m s–1 and rated is 12.8 m s–1. The 

significantly positively skewed distributions show that turbine operations were possible about 

25%–30% of the time. The most frequent higher wind speeds, like those at the California wind 

farm, occur after sunset and before local midnight. This was also the period when conditions 

were often too severe for the turbine to operate. 

The corresponding diurnal distribution of RiTL is shown in Figure 4-30. Here the upper limit of 

the CRR stability range (RiTL = +0.05) and the nominal upper limit for significant turbine 

response (RiTL = +0.10) are shown as dot-dashed and dot-dot-dashed lines. Also, a value of RiTL 

= +0.25 is indicated with a dashed line and identified as Ric. This is the theoretical upper limit 

for turbulence to exist and is often referred to the critical Richardson number. These distributions 

indicate that the flows resided within an RiTL range of 0 to +0.10, a significant amount between 

the time of local sunset and sunrise (~ 1700 to 0700 local time) and between 1700 and 0300 

hours in particular, which also often corresponds to the periods with the strongest winds. 

In Figure 4-31 we plot the observed diurnal variations in the tails of the blade root FBM load 

distributions and the corresponding number of data hours associated with each of the hourly 

periods. As shown in Figure 4-31b, on average each hourly bin had about 10–12 hours of data 

except just after sunrise (~ 0700 hours) and from 2100 to 2300 hours, when severe wind 

conditions precluded the turbine from operating numerous times. Using the P95 quantile of DELs 

of 240 kNm or more as a high damage/load criterion, we see three main periods of an hour or 

more when this level is exceeded. They include between 0100 and 0300 hours, 0700 and 0900 

hours (at sunrise and for 2 hours after), and 2000 and 2100 hours, which in all likelihood would 

also include the 2200 and 2300 hour bins if the turbine had been able to operate more. In Figure 

4-32 we repeat Figure 4-31a as Figure 4-32b to allow an ease of direct comparison with the 

matching diurnal P10, P25, P50, P75, and P90 quantile distributions of RiTL. We annotated this 

figure with a horizontal white dot-dashed line corresponding to RiTL = +0.02 that represents the 

maximum dynamic response seen on the Micon 65/13 turbines in California. We also used 

dashed lines to identify the RiTL values of +0.05 and +0.10 that indicate the upper limits of the 

CRR and CRRH stability ranges. The highest values of the P95 FBM DELs, with one exception, 

occur during the hours in which the value of RiTL falls within the CRR stability class at least half 

the time. The exception is the largest P95 value, which occurs in the 0900 hour bin. This is when 

the boundary layer is in transition from nocturnal stable to daytime convective and when we 

have observed significant transient turbine loading events. 

97
 
 

Figure 4-29. Boxplot presentation of probability in diurnal variation in NWTC 50-m mean wind 

speed observed during LIST observational period from October 1999 to May 2000. The horizontal 

dashed line represents rated wind speed for the ART. The cut-in wind speed was about 6 m s–1. 

Figure 4-30. Boxplot presentation of probability distributions of diurnal variation of RiTL when ART 

was operating during LIST experiment 

98 
 

(a) 

(b) 

Figure 4-31. Diurnal variations in (a) P90 and P95 quantiles of ART root FBM DEL distributions 

and (b) corresponding total number of hours of available observations for each time hour period. 

The few observations from 2100 to 2400 hours are the consequence of wind conditions that were 

often too severe for turbine operation. 

99
 
 

 

 

(a) 

(b) 

Figure 4-32. Diurnal variation in quantiles of (a) RiTL during ART operation and (b) corresponding 

P90 and P95 quantiles of probability distributions of observed root FBM DELs. The low values in 

(b) between 2200 and 2400 LST are a consequence of the turbine frequently not operating because 

of severe wind conditions. 

100
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5.0 Comparing Micon 65/13 Turbines and ART Dynamic 

Responses in Their Turbulence Operating Environments 

Our individual analyses of the dynamic responses of the Micon 65/13 turbines in the California 

wind farm and the National Wind Technology Center (NWTC) Advanced Research Turbine 

(ART) found that blade root and low-speed shaft bending loads and nacelle response dynamics, 

in addition to the mean wind speed, are highly correlated with the stability of the atmospheric 

layer in which the turbines reside. We also showed that these responses are also sensitive to the 

local turbulent shear stresses or friction velocities u* within the rotor disks, the variation of 

vertical wind speed σw, and most important, the peak values of the turbulent coherent kinetic 

energy Ecoh. For both turbine designs and operating environments, we also identified a narrow 

range of the turbine layer gradient Richardson number (RiTL) stability parameter in which the 

turbine dynamic responses were the greatest and which we refer to as the critical Richardson 

number range, or CRR. We now present direct comparisons of dynamic response sensitivities of 

the two turbine designs in their specific operating environments to ascertain just how common or 

universal they may be. 

5.1 Comparing Full-Range Stability Classes

In Figure 5-1 we compare the sensitivities of the blade flap bending moment (FBM) equivalent 

fatigue damage equivalent loads (DELs) as a function of RiTL for the two Micon 65/13 turbines 

operating in Row 37 of the California wind farm (Figure 5-1a) and the ART on Row 4 of the 

NWTC (Figure 5-1b). We annotated each plot with vertical dashed lines depicting the CRR 

stability range (+0.01 to +0.05). We also marked the value of RiTL = +0.02, where the peak 

response is seen on the Micon 65/13 turbines. 

Previously we defined the RiTL range from +0.05 to +0.10 as the critical range high, or CRRH. 

We classified the RiTL range of +0.10 to +0.25 as the STC04 or moderately stable range. These 

more stable ranges are better defined in the NWTC ART data set because (1) almost four times 

as much data are available overall and (2) many more observations exist in the CRRH and 

STC04 ranges. The fact that the Micon 65/13 turbine dynamic responses were influenced by an 

aggregate wake flow from 36 rows of upstream turbines may have a distinct influence when 

compared with the response of the NWTC ART operating in a natural inflow. These differences 

may be manifested by the distinct and rapid increase in response seen on the two Micon turbines 

compared with the ART as the stability of the inflow transitions from unstable/neutral to stable, 

seen in Figures 5-1a and b (i.e., from stability class STC02 to CRR). 

5.1.1 Turbine Dynamic Response Comparisons to Variations in Ecoh and σw 

In Figure 5-2 we further examine the response of the two turbine designs and operating 

environment by plotting the corresponding variations in the hub peak values of Ecoh and σw in 

addition to the FBM DELs. The change in peak Ecoh as the inflow becomes stable (RiTL > 0) and 

is quite noticeable especially after an RiTL value of +0.01 to +0.02 is reached, particularly in the 

variations of the FBM DELs and hub σw measured on the Micon 65/13 turbines. These 

transitions are not as abrupt for the ART, as shown in Figures 5-1b and 5-2b. The ART has a 

significant number of FBM DEL relatively higher loads (greater than 200 kNm) in the RiTL range 

101
 
Figure 5-1. Observed variations of root FBM DELs with RiTL for (a) Micon 65/13 turbines in Row 37 

of California wind farm and (b) NWTC ART operating in natural inflow at Row 4. The CRR stability 

range is identified by the vertical dashed lines and the value of peak Micon turbine response 

(+0.02) is shown as a vertical dot-dot-dashed line. 

102 
 

Figure 5-2. Comparisons of variations of hub-height peak Ecoh, root FBM DELs, and hub σw with 

RiTL observed at (a) Micon 65/13 turbines at Row 37 of California wind farm and (b) ART on Row 4 

of NWTC. The RiTL associated with maximum Micon turbine response (+0.02), the upper limit of the 

CRR range (+0.05), and the nominal upper limit of observed significant Micon dynamic responses 

(+0.10) are shown as dot-dot-dashed, dashed, and dotted vertical lines, respectively. 

103 
Figure 5-3. Comparison of vertical fluxes of peak coherent turbulent kinetic energy (

w′Ecoh) inflows to (a) hub he

turbine rotors at Row 37 in California wind farm; and (b) at the bottom (15 m), hub (37 m), and top (58 m) of NWTC 

The downward fluxes are shown in the left column and the upward in the right column. The CRR stability range i

dashed vertical lines. 

104 
 

 

Figure 5-4. Observed variations of root FBM DELs with mean and peak values of vertical flux of 

Ecoh (w’Ecoh) for (a,b) hubs of the California wind farm Micon 65/13 turbines and (d,e) 15-, 37- (hub), 

and 58-m heights of the NWTC ART rotor disk. Variations of the maximum values of w’Ecoh with 

the mean value for the wind farm turbines are shown in (c) and for the ART in (f). 

105 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

of −0.1 to 0 compared with the two Micon turbines. The explanation for this phenomenon can be 

seen in the strength of the vertical fluxes of Ecoh for the two locations as a function of stability 

as presented in Figure 5-3. Row 37 in the wind farm, shown in Figure 5-3a, has intense vertical 

fluxes of Ecoh, but they primarily occur within the very weakly stable range of +0.01 < RiTL < 

+0.02. Even though the most significant vertical Ecoh fluxes take place within the CRR stability 

class range at the NWTC, significant vertical fluxes occur in the unstable RiTL range of −0.10 to 

0 and are the most intense at the height of the of the top of the ART rotor. Figure 5-4 compares 

further the differences in the vertical Ecoh fluxes. Here the FBM DEL loads are plotted against 

the hub-height mean flux w E' coh in Figures 5-4a and d, and the peak values of w E' in Figures coh 

5-4b and e. In Figures 5-4c and f we plot the variations of the peak values of w E' with ' . coh w Ecoh 

In Figure 5-4a we see that at Row 37 in the California wind farm the FBM DEL loads on the 

Micon 65/13 turbines are affected by a persistent contribution of a downward flux of Ecoh.. In 

Figure 5-4d we see that at the NWTC the loads on the ART are influenced by both upward and 

downward mean fluxes that increase in intensity with height across its rotor disk. Figure 5-4b 

shows that the larger loads on the Micon turbines tended to be associated with larger peak 

downward fluxes of Ecoh ( w E' coh ≥ 200 m3 s

-3) compared with the smaller upward ones. In 

contrast, the largest loads seen on the ART were related to both upward and downward peak Ecoh 

transports seen at highest rotor elevation in Figure 5-4e. Figure 5-4c further demonstrates the 

existence of a persistent downward mean Ecoh flux and its influence on the largest FBM DEL 

values at Row 37 in the wind farm. Figure 5-4f underscores the bi-directionality of the mean flux 

and its nearly balanced influence on the peak largest FBM DEL values seen on the ART. It is this 

bidirectional vertical transport of Ecoh in the NWTC environment that accounts for the high 

values of Ecoh, σw, and FBM DEL loads in the weakly unstable region and is most likely a 

consequence of the dynamics of flows emanating from the major mountain range to the west. 

5.1.2 Turbine Dynamic Response to Variations in Turbulence Scaling 

Characteristics 

5.1.2.1 Hub-Height Turbulence Intensity and Friction Velocity 

Figures 5-5a and b plot the variations of the FBM DEL loads with the hub-height turbulence 

intensity (Ihub) and local turbulent shearing stress or u* for the Micon 65/13 turbines and the 

ART. As one would expect, the loads increase (albeit with broadening scatter) increase with Ihub 

in the natural inflow to the ART. By contrast, as mentioned earlier, an opposite trend is seen for 

the Micon 65/13 turbines deep within the California wind farm. We believe this to be a 

consequence of the turbulent flow within the wind farm in which σ U is larger and increases H 

more rapidly with mean wind speed than is characteristic of the natural flow seen at the NWTC. 

A nominal monotonic increase in the FBM DEL loads with hub-height (local) u* is seen in both 

the two Micon 65/13 turbines and the ART, again with a bit more scatter in the natural flow of 

the latter. 

5.1.2.2 Rotor Disk Shear Exponent and Hub-Height Mean Wind Speed 

Figures 5-6a and b present the variations of the FBM DEL loads with the rotor disk shear 

exponent α and hub-height mean wind speed UH for the Micon 65/13 turbines and the ART, 

respectively. The intense turbulent mixing between the rows of the California wind farm limits 

106
 
 

Figure 5-5. Observed variations of root FBM DELs with hub-height turbulence intensity (Ihub) and 

local friction velocity u* for the (a) Micon 65/13 turbines and (b) ART 

107 
 

Figure 5-6. Observed variations of rotor disk shear exponents (α) and hub-height mean horizontal 

wind speed UH of (a) Micon 65/13s and (b) ART root FBM DELs 

108 
 

 

 

 

the observed shear to a narrow range. At the NWTC the natural flow is more stably stratified in 

the colder months when we conducted the field campaign. This limits the strength of the vertical 

mixing and the turbine dynamic loads increase with both shear and mean wind speed. This 

difference in shear is further compared for the two sites as a function of stability in Figure 5-7. 

Figure 5-7a demonstrates the effect of the intense mixing in the flow at Row 37 of the wind farm 

with no change in the shear exponent as the stability reaches the critical range and higher. In the 

natural inflow at the NWTC, however, there is effectively a significant step increase in the shear 

exponent when the stability reaches the CRR stability range and then continues to increase with 

rising stability, as shown in Figure 5-7b. The RiTL value of +0.02 where the greatest dynamic 

response of the Micon 65/13 turbines was observed is annotated on Figures 5-7a and b. 

109
 
Figure 5-7. Comparison of variation of rotor disk shear exponents with RiTL for (a) Micon turbines 

and (b) ART 

110 
 

 

 

 

 

 

 

 

 

 

 

 

5.1.2.3 Variation of Hub-Height Friction Velocity u* with Mean Wind Speed 

The hub-height or local mean shearing stress or friction velocity u* is an important scaling 

parameter for the dynamic responses of both the Micon 65/13 turbines and the ART. Here we 

compare its variation with the hub-height mean wind speed for both locations. Figure 5-8 depicts 

the variation of the hub-height shearing stress or local u* with stability and the hub-height mean 

horizontal wind speed for Row 37 of the wind farm and the natural inflow at Row 4 of the 

NWTC. Figure 5-8a demonstrates the influence again of the cumulative wake dynamics of the 36 

rows of upwind of the Micon 65/13 turbines in the wind farm, principally as a more rapid 

increase in u* with wind speed compared with that observed in the natural flow of the NWTC in 

Figure 5-8b. 

The highest values of u* in the wind farm flow occur within the CRR stability regime and 

coincide with the maximum observed turbine dynamic response at a value of RiTL of +0.02, 

indicated by the red dot-dot-dashed line in the upper leftmost graph of Figure 5-8a. Although the 

upper range of positive stability is limited in the wind farm data, the rapid decrease in u* with 

increasing stability compares favorably with that observed at the NWTC in the upper rightmost 

panel of Figure 5-8b. Although not as clear as that in the wind farm, the peak u* value in the 

NWTC natural inflow also seems to occur at the same RiTL value, indicating that similar 

turbulence dynamics are occurring. 

5.2 Comparing Hourly Diurnal Variations of Root FBM DEL Responses 

Figures 5-9e and f compare the hourly diurnal variations in the FBM DEL [] seen in the two 

Micon 65/13 turbines and the ART. In addition, Figures 5-9a and b plot in the topmost row the 

corresponding diurnal variations of the Micon 65/13 hub-height and ART disk-averaged values 

of the mean vertical momentum flux uw ' ' , the hub-height values of vertical wind speed standard 

deviation σw. Figures 5-9c and d present in the center row the values of RiTL and Micon hubheight and ART disk-averaged values of the mean buoyancy flux wT ' ' . The nominal times of 

the local sunrise and sunset are indicated by vertical blue lines. 

We now examine the periods with the highest loads (>20 kNm for the two Micon turbines and 

>250 kNm for the ART) and the associated turbulence parameters for each site. Starting with 

uw ' ' [] and σw [] in the top row, the high loads are associated with large values of both 

variables with the wind farm wake flow having the greater absolute levels. In the second row, the 

RiTL values [] occur often within the CRR range and the buoyancy flux wT ' '[] is negative in 

the wind farm wake and both positive and negative, with the latter more frequent at the NWTC. 

The peak values of Ecoh [] shown in the bottom row (Figures 5-9e and f) for the wind farm are 

all greater than the significant response threshold of 10 m2 s

-2 for the entire diurnal period. For 

the ART, however, the high load records are associated with Ecoh values well exceeding this 

threshold, but the periods of lower response are dominated with values that are below the 

significant level. So similarities exist, but so too do some fundamental differences in the 

atmospheric dynamics associated with the high response loads at each location. 

111
 
 

 

Figure 5-8. Observed variations of hub u* values with RiTL and hub mean horizontal wind speed 

(UH ) for (a) Row 37 of wind farm and (b) upwind of ART. The vertical red dashed lines shown in 

the upper row of graphs correspond to the value of RiTL (+0.02) in which the maximum dynamic 

response of the Micon turbines was observed. 

112 
Figure 5-9. Comparison diurnal variations of root FBM DEL responses for (e) Micon 65/13 turbines 

and (f) ART with (a,b) u w' ' and σw, (c,d) RiTL and buoyancy flux ( wT ' ' ). Nominal sunrise and 

sunsets are indicated by solid blue vertical lines. The critical stability values ranges (RiTL = +0.02, 

+0.05, and +0.10) are shown as horizontal lines in (c,d). Disk-averaged values of σw, u w' ' , and 

wT ' ' are used for the ART variables. 

113 
 

 

 

 

 

 

 

 

 

 

5.3 Defining Common Turbulence Characteristics

Comparing the inflow turbulence characteristics associated with the blade root FBM equivalent 

fatigue damage measured on the Micon 65/13 turbines immersed in an internal wind farm wake 

flow and the ART operating in a high turbulent but natural flow, we note the following: 

•	 The turbines respond in a very similar manner when operating in the STC02, CRR, 

CRRH, and STC04 stability classes, indicating that similar atmospheric dynamics are 

present. 

•	 The observed FBM fatigue damage levels in the turbines at both sites are strongly 

correlated with the peak values of Ecoh, with greater values seen in the natural flow at the 

NWTC. 

•	 The intense vertical mixing present within the wind farm flow limits the vertical shear; at 

the NWTC the shear is highly correlated with the stability classification. 

•	 The vertical transport or flux of Ecoh is an important parameter in the level of turbine 

response at both sites, but the wind farm is characterized by a persistent mean downward 

Ecoh flux and at the NWTC both upward and downward fluxes are involved. 

' '

turbine rotor disks are significant contributors to the turbine dynamic response. 

• The variations of the vertical wind speed (σw) and buoyancy flux ( wT ) within the 

5.4 Comparing CRR Turbine Response Scaling Parameters

We have seen that the most significant turbine responses in terms of peak loads and fatigue 

damage occur in both the California wind farm Micon 65/13 turbines and the NWTC ART 

within the CRR defined by the RiTL range of +0.01 to +0.05. It is useful to focus on the 

distributions of the turbulence parameters shown to scale the turbine dynamic response within 

the CRR range at both sites. 

Figure 5-10 shows the diurnal variation of the probability of CRR conditions at the site of the 

Micon 65/13 turbines and in the inflow of the ART. With the exception of the high probability at 

0100 hours at the California wind farm, the distributions are quite similar. CRR stability 

conditions are most likely to occur from late in the afternoon to around local sunrise, a period 

that coincides with a stable atmospheric boundary layer. Figure 5-11 plots the probability 

distributions of the hub-height U component for the available data populations in the CRR. In 

both cases the most frequent mean speeds occur at just below rated speeds and with equal 

probability at rated speeds. This is a sensitive wind speed range on most wind turbine rotors, 

where transient loading from unsteady aerodynamic processes can be significant. 

Figure 5-12 plots the rotor thrust coefficient CT for the NREL 7.9-m thin airfoil blades used on 

the Micon 65/13 turbine. For wind speeds between about 10 and 13 m s–1, there is a maximum 

rate of change (the steep slope of line on the diagram) in the thrust loads with speed on the 

turbine rotor. The speed also has a high probability of occurrence in the CRR stability range, as 

shown by Figure 5-11, and is most likely a contributor to the high level of turbine dynamic 

114
 
Figure 5-10. Diurnal hourly probability of occurrence of CRR stability class conditions as seen for
 

Micon 65/13 turbines on Row 37 of California wind farm and for ART on Row 4 at NWTC
 

115 
Figure 5-11. Observed hub-height mean U-component wind speeds probability distributions in the 

CRR stability range for the Micon 65/13 turbines and for ART. Each has been fitted with a 

Gaussian distribution, shown as solid lines. The rated wind speeds for the Micon 65/13 turbine 

equipped with the NREL rotor and the ART are shown as vertical dashed lines. 

Figure 5-12. Variation of thrust coefficient CT with mean wind speed for Micon 65/13 turbine with 

NREL rotor. Highest probable mean U wind speed in data set shown as vertical dot-dot-dashed 

line. (CT data source: J. Tangler, NREL) 

116 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

response observed. We do not have a CT curve for the AeroStar and ART rotors, but they are 

likely to be somewhat similar depending on the blade shape and airfoil sections included. The 

ART blades were collective pitch controlled, but fluctuations at the most frequent peak wind 

speed are centered below rated at about 11.5 m s–1. The most frequent speeds in the CRR range 

extend over a slightly broader range of about 9.5 to 14 m s–1 compared with the NREL Micon 

65/13 rotor. During the testing of this turbine, significant audible noise level emissions were 

being radiated from the blades just as the controller began to pitch them to control peak power. 

Such emissions are indicative of the occurrence of significant unsteady blade loads. 

Figure 5-13 shows the frequency/probability distributions of u* within the CRR stability range 

for the wake inflow to the Micon 65/13 turbines and the natural inflow to the ART. 

Unmistakably, the turbulent shearing stresses are much higher within the wake flow entering the 

Micon turbines than are usually present in the natural flow upstream of the ART. Neither the 

wind farm nor NWTC hub local u* distributions are Gaussian in the strictest sense, but the wind 

farm could be considered at least “quasi-Gaussian.” The u* distribution in the inflow to the ART, 

however, is significantly skewed to higher values and therefore is certainly not Gaussian within 

the CRR stability range. 

Figure 5-14 presents the frequency/probability distribution of the hub peak values of Ecoh within 

the CRR stability range for the two sites. Although the upstream turbine wake flow into the two 

Micon turbines contained higher levels of Ecoh on average than the natural flow into the ART, 

the latter turbine was subjected very high transient values occurring much less frequently. These 

peaks are strongly correlated with the vertical fluxes of Ecoh shown in Figure 5-15. Figure 5-15a 

shows that the frequent value of peak Ecoh in the Micon inflows is associated with high 

occurrence of downward w E' coh , whereas both vertical and downward mean fluxes are 

contributing to the peak Ecoh values in the inflow to the ART. Figure 5-15b shows that although 

these Ecoh peaks observed in the Micon wake inflow are the result of both positive and negative 

maximum fluxes of Ecoh, downward ones occur more frequently. In the case of the ART natural 

inflow, however, these more infrequent Ecoh peaks are the consequence of more or less equally 

likely vertical and downward maximum values of w E' coh . Thus the presence of multiple rows of 

turbines ahead of a downstream turbine can significantly modify the vertical transport 

characteristics of coherent turbulent kinetic energy into the rotor. 

5.5 Comparing Probability Distributions of Micon 65/13 Turbines and ART Root 

FBM Responses by Stability Class

Figure 5-16 shows the observed cumulative probability distributions of the root FBM DELs in 

the left column and peak loads in the right column for the two Micon turbines and the ART. The 

distributions for the available populations for each turbine are plotted in light gray. The 

distributions associated with the stability classes STC02 (green open triangles), CRR (red open 

circles), CRRH (blue open diamonds), and STC04 (black open squares) are plotted atop the 

available populations. The STC04 stability class is not given for the two Micon turbines because 

of too few observations. The diagonal line across each diagram designates the expected 

cumulative probability of a true Gaussian process and is a reference to ascertain the degree to 

which the observed processes are normally distributed. 

117
 
 

 

 

 

 

 

 

 

None of the distributions displayed in Figure 5-16 are representative of a true Gaussian or 

normal process. The loads measured on Micon 65/13 turbines in the wind farm wake flow, 

particularly the DELs, generally are the closest, especially in the high loading tails. In contrast, 

the distributions in Figures 5-16e and f measured on the ART in a natural flow exhibit significant 

non-Gaussian behaviors characterized by the negative skew. We see more small loads and fewer 

large ones than would be expected from a normal process. The Micon loads in the stable CRR 

and CRRH classes are similarly distributed in the high loading tails. The effect of stability 

stratification on the ART is more pronounced as the amplitudes decrease with increasing stability 

but not so much in the distribution shapes themselves. As in the Micons, the ART high loading 

tails in the STC02 and CRR converge. 

It is not clear if the differences highlighted by these results are a consequence of (1) operations in 

a wind farm wake environment as opposed to a rigorous but naturally occurring inflow; (2) 

three-bladed stall controlled rotors with a rigid hub design versus a two-bladed pitch controlled 

rotor with a teetered hub; or (3) some combination of both. For example, one could conclude that 

the skewed distribution seen in the ART response could be related to the teetering hub removing 

the large once-per-revolution loads but having no ability to minimize turbulence scales smaller 

than the rotor diameter. Similarly, one could hypothesize that the near-Gaussian response seen in 

the Micon turbines is linked to a combination of stall control and a rigid hub. Some of these 

questions could be answered if accurate design models of these two turbine designs were 

modeled with a suitable multibody dynamic code excited by a realistic turbulent inflow 

simulation of both operating environments. 

118
 
 

 

Figure 5-13. Observed hub-height shearing stress or u* probability distributions in CRR stability 

range for the Micon 65/13 turbines and ART. Each has been fitted with a Gaussian distribution 

shown as solid lines. 

Figure 5-14. Observed hub-height shearing peak Ecoh probability distributions in CRR stability 

range for Micon 65/13 turbines and ART. Each has been fitted with a Gaussian distribution, shown 

as solid lines. 

119 
 

(a) 

(b) 

Figure 5-15. Observed hub-height fluxes of w’Ecoh for CRR stability range at Row 37 of the wind 

farm and Row 4 of the NWTC: (a) means and (b) peak values. Each has been fitted with a Gaussian 

distribution, shown as solid lines. 

120 
 

Figure 5-16. Comparison of Micon 65/13 turbine and ART cumulative probability distributions of 

root FBM DELs and peak loads for available populations [] and stability classes STC02 [], 

CRR [], CRRH [  ], and STC04 [] . Micon 65/13 with NREL rotor FBM: (a) three-blade averaged 

DELs; (b) three-blade peak. Micon 65/13 with AeroStar rotor FBM: (c) three-blade averaged DELs; 

(d) three-blade peak. NWTC ART FBM: (e) DELs; (f) peaks. 

121 
 

 

 

 

 

 

 

 

 

 

 

 

 

6.0 Atmospheric Dynamics Associated with Turbine Response 

6.1 Comparing Turbine Responses by Stability Class

In Section 5 we found that the dynamic responses expressed in fatigue damage and peak loads of 

the California wind farm Micon 65/13 turbines and the National Wind Technology Center 

(NWTC) Advanced Research Turbine (ART) were similar when correlated against several 

turbulence parameters and atmospheric scaling parameters. Most important, we found that a key 

parameter influencing the severity of the response was the dynamic stability of the vertical 

atmospheric layer above the local ground level of the turbines. We expressed this parameter as 

the turbine layer gradient Richardson number, RiTL. Our analysis showed that the turbine 

responses could be further subdivided into at least five stability classification ranges that applied 

to both the Micon 65/13 turbines and the ART. Table 6-1 lists these ranges. 

Table 6-1. Turbine Layer Stability Classifications for Turbine Response Correlations 

Stability Class Designation Range 

Moderate to Weak Unstable Class, STC02 –1 < RiTL ≤ 0.00 

Weakly Stable Critical Range, CRR +0.01 ≤ RiTL < +0.05 

Weakly Stable High Range Critical, CRRH +0.05 ≤ RiTL < +0.10 

Moderately Stable Range, STC04 +0.10 ≤ RiTL < +0.25 

Very Stable Range, STC05 +0.25 ≤ RiTL < +1.0 

Only 12 observations were available in the moderately stable STC04 classification in the Micon 

65/13 data set and none in the very stable STC05. Similarly, the ART data set had only 17 

observations available in the very stable STC05 classification. We used the few STC02 

observations for the Micon 65/13 correlations for an estimate of completeness, but we advise 

caution in the level of acceptance. For the ART correlations, we decided to not use the few very 

stable STC05 observations because the other four classes encompassed 95% of the available data 

set, and the mean wind speeds for STC05 were very low. We also found that the maximum 

turbine dynamic responses for the Micon turbines and the ART occurred near RiTL = +0.02. 

Figure 6-1 shows boxplot probability distributions of the root flap bending moment (FBM) 

damage equivalent loads (DELs) and peak load responses for the National Renewable Energy 

Laboratory (NREL)-rotor equipped Micon turbine and the ART for each stability class. Figure 6­

2 shows the corresponding distributions for the hub-height mean U-component wind speeds, 

rotor disk shear exponent, and hub mean buoyancy fluxes ( wT ' '), and Figure 6-3 plots the hub 

peak negative and positive vertical Ecoh fluxes ( w E' ). As shown in Figures 6-1 and 6-2, the coh 

highest loads occur in the weakly stable CRR range, which also has the highest mean wind 

speeds. Significantly, in both cases, a greater percentage of these higher load distributions occur 

122
 
m

4 50 

kN

NREL Rotor Peak Root FBM 700 Peak FBM Load 

36 

32 600 

28 500 

24 

400 

20 

16 300 

12 

200 

8 

100 

4 

STC02 CRR CRRH STC04 STC02 CRR CRRH STC04 

Stability Class Stability class 

NWTC ART Turbine Response San Gorgonio Micon 65 Turbine Response 

24 NREL Rotor Root FBM 3-Blade Mean DELs Root FBM DEL Distributions 300 

20 

250 

16 

200 

12 150 

8 100 

Figure 6-1. Boxplot probability distributions of observed root FBM DELs and peak load responses 

by stability class for California wind farm Micon 65/13 (NREL rotor) turbine and NWTC ART. The 

dots represent values outside the P10–P90 range indicated by the whiskers. 

123
10 

2 

4 

14 Hub Mean U 

San Gorgonio Micon 65 Turbines Row 37 

18 

20 

 Hub Mean U

NWTC ART Turbine Row 4 

12 16 

14 

-1 ms oK-ms-1 

-1 ms

12 

10
 

8
 8 

6 

6 

4 

0.30 0.20 Rotor Disk Layer  IEC NWP Rotor Disk Layer 

0.25 0.18 

IEC NWP 0.20 0.16 



0.14 0.15 1/7 

0.12 0.10 

0.10 0.05 

0.08 

0.4 

Hub Mean w'T' Hub w T' ' 8 

0.3 

0.2 6 

oK-ms-1 

0.1 

0.0 

-0.1 

-0.2 

STC02 CRR CRRH STC04 STC02 CRR CRRH STC04 

Stability class Stability class 

Figure 6-2. Probability distributions of observed inflow hub-height mean U-component, rotor disk

shear exponent and hub mean vertical buoyancy flux by stability class for Micon 65/13 (NREL 

rotor) turbine and the ART. The dashed lines indicate the rated wind speeds. The boxplot

nomenclature is the same as for Figure 6-1.

124 
 

 

 

 

 

 

 

 

 

 

 

 

during at or below rated wind speed inflow conditions. In the wind farm, the intense vertical 

mixing caused by the high air and surface temperatures is responsible for the strong positive 

mean buoyancy. These buoyant motions combined with the upstream turbine wakes limit the 

vertical shear exponent α to the narrow range shown in Figure 6-2. The character of the 

buoyancy and to a lesser extent the shear in the critical Richardson number range or CRR is, 

however, quite different (we cannot make a judgment about the STC04 class because of the lack 

of observations). We note that the shear is the largest of the stability classes, and the mean 

buoyancy flux wT ' ' distribution is much more negatively skewed relative to the STC02 and 

CRR High, or CRRH, stability classes but has very long tails (high kurtosis). The latter is 

indicative of large buoyancy fluxes of short duration. In contrast, the shear in the natural inflow 

into the ART increases near monotonically with increasing stability that is much more Gaussian 

or normally distributed. Only the unstable class STC02 has a significant frequency of positive 

mean buoyancy occurrences at hub height. Here the mean buoyancy distribution in the CRR 

stability class has long negative tails, indicating periods of high buoyancy damping. 

In Figure 6-3 we present box plots of the observed probability distributions of hub-height peak 

values of w E' measured in the inflow of the Micon turbines and the natural inflow of the ART coh 

stratified by stability class similar to those plotted in Figure 5-3. Here we see that the peak Ecoh 

vertical fluxes at hub height in the wind farm are strongly skewed downward, with the largest 

range in the CRR stability range. By comparison, these peak fluxes in the natural inflow to the 

ART are nearly normally distributed, particularly for the most stable CRRH and STC04 classes. 

The CRR stability range where the largest turbine response is seen in Figure 6-1 has the largest 

tails, which are approximately symmetrically distributed. In the wind farm and natural inflows, 

the impact of increased stability and its associated damping effects are well demonstrated in the 

CRRH and STC04 classes. Figure 5-15 presents observed probability distributions of the vertical 

fluxes of the mean and peak values of hub-height Ecoh ( w E' and ' respectively) for the coh w Ecoh 

CRR stability range. 

We found earlier that the dynamic responses of both the Micon turbines and the ART were very 

sensitive to peak values of Ecoh. We compare probability distributions of the root FBM DELs 

with the corresponding distributions of hub-height peak Ecoh for each of the stability classes in 

Figure 6-4. Here we see that both the root fatigue loads and peak Ecoh distributions have the 

largest positive tails (high kurtosis) in the CRR stability range, which has the smallest negative 

buoyancy turbulence damping (small positive values of RiTL) associated with it. This indicates 

these turbines when operating in the CRR stability range are subject to intermittent intense levels 

of coherent turbulence that result in high loading events more often than in the other stability 

classes. The damping impact of greater stability is most noticeable in the natural inflow to the 

ART in classes CRRH and STC04 where the body of the probability distributions remains below 

the significant peak Ecoh response threshold (dashed line). A similar but much less distinct trend 

is evident in the upstream wake inflow to the Micon turbine. Here the entire distributions of the 

observed peak Ecoh values remain higher than this threshold, with a much smaller variation 

between the CRR and CRRH stability classes. This suggests that this low variation seen between 

the stability classes is the consequence of another source of coherent turbulence in addition to 

that being locally created or being carried in the upstream wake flow within the turbine rotor 

125
 
0 

San Gorgonio Micon 65 Turbines Row 37 NWTC ART Turbine Row 4 

Hub Peak w'Ecoh Hub Peak w'Ecoh 500 500 

400 400 

300 300 

200 200

100 100

3 -3 m s 

3 -3 m s

0 

-100 -100 

-200 -200 

-300 -300 

-400 -400 

-500 -500 

STC02 CRR CRRH STC04 STC02 CRR CRRH STC04 

Stability Classification Stability class 

Figure 6-3. Probability distributions of inflow hub-height peak Ecoh vertical fluxes (w′Ecoh) for 

Micon 65/13 (NREL rotor) turbine and ART. The boxplot nomenclature is the same as for Figure 6­

1.

126
40 

80 

San Gorgonio Micon 65 Row 37 

80 

NWTC ART Turbine Row 4 

Hub Peak Ecoh 

60 60 

kNm 

m2

s-2 

2 -2 m s 

40 

20 20 

0 0 

22 

300 

20 Blade Root FBM DELs 

18 250 

16 

14 

12 

kNm 

200 

10 

150 

8 100 

6 

4 

STC02 CRR CRRH STC04 

50 

STC02 CRR CRRH STC04 

Stability class 

Figure 6-4. Comparison of probability distributions of Micon 65/13 (NREL rotor) turbine and ART 

hub peak Ecoh (upper panels) and blade root FBM DELs (lower panels) by stability class. Dashed 

line in upper panels (peak Ecoh) represents the significant turbine dynamic response threshold. 

The boxplot nomenclature is the same as for Figure 6-1.

127
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

layer, i.e., a significant downward flux or transport of peak Ecoh from the boundary layer above 

the turbine rotors which is unambiguously demonstrated in Figure 6-3. For the ART, vertical 

transport of peak Ecoh is also operative, but high values are likely to be transported upward as 

well as downward within the turbine rotor layer. This further suggests that local creation of the 

coherent turbulence within the rotor disk layer is more important in the natural inflow to the 

ART. 

6.2 Defining Role of Turbulent Buoyancy in Turbine Dynamic Response

The characteristics of the dynamic responses of turbine components are significantly influenced 

by the dynamic stability of the depth of the atmospheric boundary layer in which the turbines 

reside, i.e., expressed by RiTL. The relationship of RiTL to the turbulence kinetic energy budget 

within the turbine layer is discussed in sections 6.2.1 and 6.2.2. 

6.2.1 Relationship between Shear and Buoyancy Turbulence Generation

RiTL is the ratio of turbulence generation/destruction to that being generated by shear over the 

atmospheric layer occupied by a turbine. Large, convective turbulent eddies grow when it is 

negative because of a positive (upward) flux of buoyancy. Conversely, when it is positive, the 

size and velocities of the largest eddies are damped (growth restricted or suppressed) and 

velocities are reduced first, which extend to smaller ones as RiTL increases (becomes more 

positive) because of the downward flux of buoyancy. Figure 6-5 shows this relationship by the 

contours of wT ' ' for the measured natural inflow to the ART on Row 4 of the NWTC at the 

bottom, hub, and top of the rotor. The warmer colors (yellows and reds) represent positive 

(upward) values and the cooler ones (light blue to purple) indicate negative buoyancy 

(downward) fluxes with white being extremely weak or zero. The CRR stability range is 

indicated by a pair of vertical dashed red lines. The value of RiTL = +0.02 where the maximum 

turbine response often occurs is marked with a dash-dot-dotted line. Finally, the value of RiTL = 

+0.10, above which the turbine response is generally minimal, is identified with a dotted line. 

The contours of Figure 6-5 clearly demarcate the buoyancy fluxes in the unstable (left) and 

stable (right) regimes and the corresponding vertical momentum fluxes or shear stresses. Neutral 

conditions (RiTL ≅ 0) are clearly identifiable where turbulence generation is solely caused by 

shear. The weakly stable CRR range is obvious, as is the increasing negative flux gradient in the 

CRRH range from RiTL = +0.05 to +0.10. Finally, at RiTL values greater than +0.10 the buoyancy 

flux reaches its negative maximum in conjunction with a high shearing stress. Figure 6-5 also 

shows that significant vertical buoyancy flux and shear stress gradients exist across the rotor 

under the most unstable (RiTL < –0.2) and stable (RiTL > +0.2) regimes, and these gradients’ 

intensity decreases with height. 

6.2.2 Buoyancy Damping and Length Scale

To obtain a measure of the spatial scale of vertically buoyant velocity motions in stable flow, we 

employ the buoyancy length scale Lb defined as in Stull (1988): 

σ w Lb = . (6-1) Nbuoy 

This scale is measure of the thickness of layers (the maximum vertical displacement of air 

parcels) of stratified turbulent layers and is the wavelength of the dominant instability mode 

(Rosenthal and Lindzen 1983; Smith et al. 2001). If we calculate Lb over the turbine layer depth 

128
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

and normalize it with the rotor diameter D, we can relate the dominant vertical buoyancy spatial 

mode to the dimensions of the turbine rotor expressed as Lb /D. In Figure 6-6 we display the 

probability distributions of the observed Lb /D ratios for the Micon 65/13 turbine equipped with 

the NREL rotor and the ART for CRR, CRRH, and STC04. Noticeably this ratio falls within the 

P25–P75 percentile range (Q3–Q1 interquartile range) or 50% of the time in the CRR stability 

range. This says that the dominant vertical scale of the damped turbulent eddies (vertical 

motions) at the hub height on the Micon turbine and within the rotor disk of the ART is 

equivalent to the rotor diameter about half the time in the CRR stability range. As the turbine 

layer becomes more stable and the damping increases, the expected or characteristic vertical 

scale decreases to 0.6 D and about 0.35 D in the CRRH and STC04 ranges, respectively. The 

observed ranges of Lb /D in the wake inflow to the Micon turbine are smaller than in the natural 

flow into the ART where the scale of the vertical motions can exceed 2 D in the CRR range. 

In the upper panels of Figure 6-7 we plot the variation of the observed Lb /D parameter for the 

Micon turbines and the ART with respect to stable range RiTL. In the lower panels we plot the 

corresponding root FBM DELs with LOESS smoothed lines with a 0.3 overlap added to all. We 

annotated the figures with vertical dashed lines outlining the CRR stability range, a vertical dashdot-dotted line marking RiTL = +0.02 where the peak response seen on the Micon turbines 

occurs, and a vertical dotted line indicating RiTL = +0.10 the upper limit of the CRRH range and 

above which the turbine response generally becomes minimal. In examining the relationships for 

the Micon turbines on the left of the figure, we see that the peak turbine response occurs when Lb 

≅ D and the RiTL is between about +0.01 and +0.02. In the range +0.02 < RiTL +0.05, the 

damping increases rapidly as Lb decreases to 0.5 D. This decrease is accompanied by a reduction 

in the turbine response, as seen in the lower left panel. At RiTL values greater than +0.10, the 

buoyancy scale asymptotically approaches 0.35 D and the turbine response trends downward but 

with significant scatter. We believe this is a consequence of intense downward bursts of coherent 

turbulent energy entering the rotor disks from above (see Figure 5-3 and the left panel of Figure 

6-3). 

Comparing the data in the right-hand panels in Figure 6-7 from the ART operating in a natural, 

nonwake inflow, we see the variation of Lb /D with RiTL is very similar to that seen in the wind 

farm. In the lower right-hand panel we see that many more data points have a much greater 

scatter than those in the wind farm. Though much broader, the peak of the smooth curve resides 

in the same narrow RiTL range as in the Micon turbines, between +0.01 and +0.02. The peak 

turbine response takes place within a buoyant structure with a spatial dimension of about 1.5 D 

compared with 1.0 D for the Micon turbines. This is most likely a consequence of the larger 

ART rotor diameter operating in a more vertically heterogeneous layer. The consequences of the 

increased buoyancy damping shown in Figure 6-5 for RiTL values greater than +0.05 are quite 

marked, particularly above +0.10, and similar to that shown in Figure 6-6. Although there is 

greater scatter associated with measurements taken with a nonwake, natural inflow on the ART, 

the underlying variations with vertical stability are quite similar and suggest consistent physics 

even though the inflow environments of the Micon turbines were in many ways quite different, 

i.e., deep within the wake flow of a wind farm with 36 rows of upstream turbines and 

downstream of a major mountain range but with homogenous terrain immediately upwind. 

129
 
 

Figure 6-5. Variation of measured mean buoyancy flux ( wT ' ' ) with RiTL and mean vertical 

2 momentum flux ( u w' ' or u ) with height for natural inflow into ART. The red vertical dashed lines * 

outline the CRR stability range, the dot-dot-dash line identifies the California turbines maximum 

response, and the dotted line indicates the upper limit of the CRRH stability range. 

130 
 ART Turbine 

L b /D 

0.0 

0.5 

1.0 

1.5 

2.0 

2.5 

not defined 

San Gor NREL Rotor 

L b /D 

0.0 

0.5 

1.0 

1.5 

2.0 

2.5 

not defined 

(b) 

(a) 

STC02 CRR CRRH STC04
 

Stability class
 

Figure 6.6. Probability distributions of Lb/D ratio by stability class for (a) Micon 

65/13 turbine (NREL rotor) and (b) ART. The Lb for the Micon 65/13 turbine is 

based on the hub-height ơw and the disk-averaged ơw for the ART. 

131
 

 

Figure 6-7. Correlation of Lb/D ratios and FBM DELs with RiTL for Micon 65/13 turbines and ART. A 

trend line has been fitted to each of the distributions. 

132 
 

 

 

 

 

 

 

 

 

 

6.2.3 Effects of Turbulent Buoyancy Damping on Characteristics of Turbine 

Dynamic Response

In stable flows the buoyancy length scale Lb decreases with increasing turbine layer stability, but 

when it has roughly the spatial dimensions of the turbine rotor (Lb = D) the largest turbine 

dynamic responses occur. In Figure 6-8 we present an example using the NREL-rotor equipped 

Micon 65/13 turbine of the effects caused when the RiTL is less than the lower threshold of the 

CRR range (+0.01) and when it is greater than the maximum response value range of +0.01 to 

+0.02. Here we use a polar diagram to plot the instantaneous root FBM loads measured on each 

of the three blades as a function of the rotor azimuth. The azimuth blade order was Blade 1, 

Blade 3, and Blade 2 rotating clockwise and looking downwind in the field experiment 

nomenclature and coordinate system. The rotor loads shown on the left occurred within a record 

with a very weak stability of RiTL = +0.007 and less than the lower threshold of the CRR range. 

Here, over about half the rotor disk, the peak loads are occurring in the 15–18 kNm range. But 

for one revolution, when the blades were descending in order (Blade 1, Blade 3, and Blade 2), 

they encountered a more intense turbulence structure of sufficient dimension that all three blades 

were able to pass through it. On the right of Figure 6-8 we see another sequence in which the 

RiTL = +0.034 and is within the CRR range but is slightly more stable than the maximum 

response criticality of RiTL between +0.01 and +0.02, where damping has more influence. Here 

smaller load excursions are being induced throughout the entire rotor azimuth range, but for one 

rotation as the blades descended Blade 3 responded with a load peak of 30 kNm as it 

encountered an intense turbulent structure. This response occurred between the smaller load 

excursions seen earlier by Blade 1 and later by Blade 2. We interpreted this as Blade 3 

encountering a small but very intense turbulent structure in which Blades 1 and 2 caught only a 

piece of it because of either its residence time within the rotor disk or its physical size. The 

turbulence associated with the response seen on the left of Figure 6-8 is the result of very weak 

buoyancy damping, but that on the right is being influenced to a greater extent, with the largest 

buoyant eddies being affected the most but also allowing for the occasional intense eddy to be 

advected through the flow into the turbine rotor. 

133
 
 

Figure 6-8. Example of effects of weakly stable flow buoyancy damping on loads seen on Micon 

65/13 turbine with NREL rotor. Polar plots looking downwind of the rotor azimuth of FBM loads 

instantaneously measured on each blade. 

134 
 

 

 

 

 

 

 

 

 

In Figure 6-9 we summarize factors influencing the intensity of the root stress cycles induced in 

a turbine blade operating in a stable environment using the data from the ART. On the left of the 

diagram we plot the variation of these stress cycles (Figure 6-9a) in conjunction with the 

corresponding RiTL (Figure 6-9b), and the hub-height peak Ecoh (or CTKE) values (Figure 6-9c) 

as a function of the buoyancy length scale normalized by the disk diameter Lb /D. We previously 

found that the maximum dynamic response takes place when Lb is 1 or slightly greater. 

Following the Lb /D value vertically through Figure 6-9, we see the following: 

•	 This value intersects with the significant peak Ecoh response threshold of 10 m2 

s

–2 with 

larger loads above it and smaller ones below. 

•	 It passes through the upper end of the CRR RiTL stability range. 

•	 There is a distinct increase in the FBM cyclic stress levels at and above it. 

Figure 6-9d on the right shows that buoyancy damping increases (Lb /D < 1) in the CRRH 

stability range (+0.05 ≤ RiTL < +0.10) and more rapidly for RiTL > + 0.25. Using the data from 

both the Micon 65/13 turbines and the ART, we schematically relate observed dynamic loading 

characteristics to the degree of buoyancy damping present as a function of the RiTL in stable 

inflows in Figure 6-10. Going from left to right: 

•	 Left: many moderate intensity stress cycles interspersed with a few from long-lasting or 

dimensionally large turbulent structures 

•	 Center: many intense stress cycles but with occasional very intense turbulent structures 

that can induce significant “rare” loading events 

•	 Right: many relatively low-level stress cycles with an occasional intense loading cycle of 

short duration. 

135
 
 

 

Figure 6-9. Summary of major inflow turbulence parameters influencing ART peak root FBM (a) 

peak cyclic stresses in stable flow; (b) RiTL; (c) intensity of coherent turbulent structures given by 

hub-level peak Ecoh (CTKE); and (d) buoyancy length scale Lb /D with stability ranges shown 

136 
 

 

Figure 6-10. Schematic example of consequences on turbine FBM loads from stable turbine layer 

buoyancy damping using both Micon 65/13 turbines and ART 

137 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6.3 Atmospheric Dynamics Associated with CRR Stability Range

We showed that the CRR stability range is truly critical in terms of the nature of the dynamic 

loading response of wind turbine components. The question then is what are the atmospheric 

turbulence dynamics that are responsible for creating the turbulent flow conditions within this 

important range? From our analysis of the San Gorgonio and NWTC inflow data, and based on 

Figures 6-2 and 6-3, we know the following: 

•	 The turbine layer Richardson number stability parameter covers a narrow range of +0.01 

< RiTL < +0.05. 

•	 The majority of the hub-height mean wind speeds are at or below rated. 

•	 Vertical shear exists. 

•	 For the NWTC, there is a predominant downward buoyancy flux that applies a
 

stabilization action (damps) the largest turbulent eddies.
 

•	 The highest mean wind speeds occur in this stability range. 

•	 The highest values of CTKE or Ecoh occur in this range, suggesting the frequent
 

appearance of the coherent turbulent structures seen in Figures 3-7, 3-8, and 3-9.
 

•	 The buoyancy length scale, Lb, was the same as the rotor disk diameter about half the 

time (Figure 6-6). 

After reviewing this information, we concluded that we were dealing with some form of shear 

instability within the flow entering the turbine rotors in stable conditions. Under stable 

conditions, the boundary layer flow tends to form into parallel, stratified layers in the absence of 

the vertical mixing associated with the unstable, convective boundary layer. With the right 

conditions, perturbations moving through the flow within these layers can initiate turbulent 

disturbances that grow in size and intensity with time. Two types of instabilities are common in 

the stable lower boundary layer in which wind turbines reside: the Kelvin-Helmholtz Instability 

(KHI) and the internal gravity wave instability (GWI) that form through the action of buoyancy 

in vertically sheared flows. 

KHI occurs in shear layers in which intense, 3-D coherent turbulent structures are created. The 

majority of the turbulent kinetic energy is contained within this shear layer and decays rapidly 

away from it. The KHI coherent structures (billows) follow a life cycle that typically lasts 15–30 

minutes, which is why they are often described as turbulent patches. This cycle includes the 

initial rollup formation, a rollover or breaking that becomes very turbulent (turbulent 

breakdown), and finally a decay. During this last phase the energetic turbulence is mixed out, 

returning the turbulent kinetic energy back into a form of potential energy. The life cycle of an 

individual Kelvin-Helmholtz (K-H) billow is typically much shorter than the total length of the 

instability as a whole, often in the tens of seconds. 

Internal GWI also occurs in shear layers, but the turbulent structures are often much less 

energetic, more 2-D, and much thinner than K-H billows. Although the KHI process takes place 

rather quickly, the GWI turbulent structure grows much slower and can persist for many hours. 

In contrast to KHI, the kinetic energy associated with GWI propagates away from the formation 

layer. The question is which of these types of shear instability is the dominant turbulence 

138
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

generation mechanism in the important CRR stability regime and how does it relate to the other 

more stable ones, CRRH and STC04? 

6.3.1 Dynamics of KHI

Linear analysis has been successfully applied to the initial stage of instabilities forming in a 

stably stratified sheared flow (Miles 1961; Howard 1961). The schematic diagram of Figure 6-11 

illustrates the mean vertical profiles of wind speed and temperature of such a flow into a turbine 

rotor disk of diameter D. These are the background or reference conditions that determine if 

intense shear alone or in combination with small turbulent perturbations will grow or be 

suppressed with time. These regions of instability occupy finite space and the K-H billows or 

coherent patches of turbulence grow within them. Smyth (2004) points out that it is the fastest 

growing instability mode that fills this region of KHI. Although the coherent patches themselves 

are fully 3-D turbulent structures, the KHI process itself is essentially 2-D (i.e., characterized by 

the streamwise and vertical turbulent wind components u′ and w′, with emphasis on the latter). 

The theory of billow growth is an eigenvalue problem that is represented as a spectral 

superposition of temporally growing normal modes (Smyth 2004). The normal mode solution is 

of the form 

exp[ ik x ( − ct )] , (6-2) 

where k is the wavenumber, the complex phase speed is c c = r + ci , and t is time. Here cr is the 

perturbation phase speed in the direction of the background flow and kci is its rate of growth; i.e., 

growing modes are characterized by ci > 0. Howard (1961) showed that the maximum growth 

within a shear layer for a mode with wavenumber k is limited by (Kundu 1990, p. 387): 

kci < (k / 2)( U −U ) . (6-3) max min 

A necessary but not sufficient condition for instability (growing perturbations) within a stably 

stratified shear layer is Ri < 0.25. Figure 6-12, adapted from Figure 11 of Rosenthal and Lindzen 

(1983), shows the maximum K-H mode growth rates as a function the shear layer Ri. The Miles 

and Howard (1964) curve is for an infinite stratified fluid that resides only within the shear layer 

and corresponds to the wavelength of the most unstable K-H mode. The Lindzen curve is based 

on observations that encompassed a broader region (Lindzen 1974). Figure 6-13, adapted from 

Figures 3, 6, and 8 of Rosenthal and Lindzen (1983), plots the range of K-H mode wavenumbers 

( reciprocal wavelengths) and their corresponding growth rates for shear layer Ri values of 0.05, 

0.10, and 0.15. A shear layer stability of Ri = +0.05 has the broadest wavenumber (wavelength) 

range of unstable normal modes, with the fastest growth rates associated with the highest 

wavenumbers (shortest wavelengths). As the layer stability increases, the peak mode growth rate 

decreases and the corresponding range of unstable wavelengths becomes narrower. 

We can put these relationships into perspective relative to stability classes for the ART in Figure 

6-14. Here we adapted Figure 3 from Hogg and Ivey (2003) by rescaling the wavenumber of the 

139
 
 

 

 

Height (

z) 

U = tanh(z) 

T = tanh(z) 

↑

}D 

U(z) →

T(z) →

Figure 6-11. Schematic representation of vertical profiles of mean wind speed U(z) and 

temperature T(z) across turbine rotor disk layer D in stably stratified shear inflow. These profiles 

represent the background or reference flow conditions on which perturbations evolve linearly 

from this equilibrium state. 

140
 
 

 

 Source: Adapted from Rosenthal and Lindzen (1983), Figure 11 

Figure 6-12. Growth rate of fastest growing K-H mode as function of shear layer Ri 

141 
 Source: Adapted from Rosenthal and Lindzen (1983), Figures 3, 6, and 8 

Figure 6-13. K-H mode growth rates and wavenumber (wavelength) range for three values of shear 

layer Ri 

142 
 

 

 

 

 

 

K-H modes into rotor diameters. The original Hogg and Ivey figure is based on a somewhat 

shallower temperature inversion relative to velocity shear layer than is illustrated in Figure 6-11. 

We believe it is useful, however, in demonstrating the interrelationships between the range of the 

fastest growing K-H modes scaled in rotor dimensions and the stability classes. Figure 6-14 

shows that the most rapid growing K-H modes occur at the low end of the CRR stability range 

and with wavelengths slightly greater than the rotor diameter at an Ri value of +0.02. This is the 

value where the maximum dynamic response has been observed on both the Micon turbines and 

the ART. The dashed line shows that maximum growth rates of the K-H modes increases with 

increasing rotor diameter. We repeat Figure 6-7 for ease of comparison. We previously noted 

that the buoyancy length scale Lb has been found to coincide closely with the fastest growing KH mode and that maximum turbine dynamic response is when Lb ≅ D as shown in Figures 6-7 

and 6-14. We see that this is in agreement with the fastest growing mode shape and range with a 

shear depth ≅ D and very low Ri values. The peak dynamic response seen on the Micon turbine 

and the ART at RiTL = +0.02 agrees well with the fastest growing K-H mode at that stability. 

Thus we must conclude that the Lb is a good predictor of significant turbine dynamic response in 

a stable atmosphere when it scales with the rotor diameter. As the stability increases the rate at 

which the mode peak grows declines and its wavelength no longer scales directly with the rotor 

diameter. This results in lower dynamic loads on the turbine. So the most energetic K-H modes, 

i.e., the fastest growing ones, have the greatest influence on the dynamic response of the 

turbines. 

143
 
 

 

 

 

 Source: Adapted from Hogg and Ivey (2003), Figure 3 

Figure 6-14. Example of K-H mode growth rates as function of shear layer depth in ART rotor 

diameters and Ri over that layer. Observed Micon turbines and ART CRR stability class is 

indicated with dashed lines, upper limit of CRRH class as the dotted line , and maximum dynamic 

response with the dot-dot-dashed line. 

Figure 6-7. Same as Figure 6-7, repeated for ease of comparison. There is a strong correlation 

between the region of fastest growing K-H modes shown above in the CRR range and the Lb /D 

and root FBM fatigue damage on both the Micon turbines and the ART. 

144 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7.0 Coherent Turbulent Structures and Turbine Response 

As a result of our field measurements in 1990 and 1999–2000, we established that the high levels 

of turbine dynamic response seen in the critical Richardson number range, or CRR, stability class 

are a consequence of Kelvin-Helmholtz Instability (KHI) taking place with the inflow to the 

turbine rotors. The characteristic billow flow structures that consist of organized or coherent 

vortical turbulence, such as those shown in Figure 3-7, are an attribute of KHI. In Section 3.5.1 

we employed wavelet analysis to decompose such time domain coherent structures into the 

corresponding spectral energy distribution in the frequency domain. This was done to understand 

the relationship between the turbulent kinetic energy distribution of these transient events and the 

corresponding stress energy frequency distribution of the dynamic response measured in the 

turbine rotors (Kelley et al. 2000). Figure 3-9 shows such a spectral decomposition of the 

dynamic stresses measured in the blade root of one of the Micon 65/13 turbines to a coherent 

turbulent structure seen in the instantaneous Reynolds stress field of the turbine inflow. Using 

this information we defined the turbulence parameter coherent turbulent kinetic energy, or Ecoh, 

as a measure of kinetic energy contained in such events. Subsequently we demonstrated that the 

turbine dynamic responses expressed as alternating load cycle spectra, equivalent fatigue damage 

equivalent loads (DELs), or peak load excursions scale with peak values of Ecoh. 

We demonstrated that KHI is the dominant source of coherent turbulence in the atmospheric 

stability range in which the greatest turbine dynamic response is observed. We then expanded 

those details to develop a further understanding of the role of coherent turbulent structures in 

inducing damaging transient stress loads on turbine components so that the TurbSim stochastic 

simulator includes the turbulence characteristics that produce them. To do that we first needed to 

be able to numerically simulate the formation and evolution of a Kelvin-Helmholtz (K-H) billow 

and then use a National Renewable Energy Laboratory (NREL) turbine design code to document 

the dynamic response to the K-H billow using a realistic turbine design. 

7.1 Kelvin-Helmholtz Billow Numerical Simulation 

At Peter Sullivan’s suggestion, he and Ned Patton of the National Center for Atmospheric 

Research (NCAR) created a large eddy simulation (LES) of the life cycle of a stationary K-H 

billow. This work was in part based on a much higher resolution (down to the dissipation scale) 

direct numerical simulation (DNS) of a nonstationary K-H billow evolution developed by Werne 

and Fritts (1999). In contrast, the minimum resolution of the NCAR LES simulation was about 1 

m where a subgrid scale (SGS) was invoked. The simulation uses a Cartesian computational 

domain consisting of (180, 60, 180) nodes in the (x, y, z) directions representing nondimensional 

dimensions of (4π, 4/3π, 25). Periodic boundary conditions are imposed on the horizontal 

directions x and y. The domain was initially stress free with fixed temperatures at the top and 

bottom. The continuously sheared streamwise background flow is defined as 

u =Uo tanh( / z h) , (7-1) 

where Uo and h are constant velocity and length scales and z is the vertical direction. The 

background temperature vertical variation is linear with T = βz where β is the mean vertical 

gradient. The gradient β is chosen to impose a gradient Richardson number (Ri) of +0.05 that 

corresponds to the fastest K-H mode growth, discussed in Section 6.3.1. A total of 6,000 time 

steps were used to describe the process. 

145
 
 

 

 

 

 

 

 

 

 

 

 

Figures 7-1a, b, and c show the stationary evolution of a K-H billow created by the NCAR LES 

simulation. These graphs present the nondimensional temperature field in the x–z plane at y = 30 

and time steps of approximately 8.4 seconds. The temperature contours are equivalent to 

streamlines and reveal the structure of the flow as it evolves. In Figure 7-1a, at t = 0, the flow in 

the shear layer is parallel and in equilibrium with warmer less dense air (red) at the top and 

colder more dense air (blue) at the bottom. A perturbation in the flow has initiated KHI by t = 8.4 

seconds, with billow development growing at the maximum rate. About 22 seconds later, at t = 

30.1 seconds, the billow has reached its maximum 2-D structure. Secondary instabilities have 

formed by t = 37 seconds and the breakdown into 3-D turbulence has begun by t = 50.9 seconds. 

The flow is fully three-dimensionally turbulent by t ≈ 70 seconds (Figure 7-1b) and reaches a 

fully mixed (saturated) state by t ≈ 170 seconds (Figure 7-1c), with internal waves forming at the 

upper and lower boundaries. Figure 7-2 shows a good portion of an actual propagating K-H 

cloud billow evolution. This photo shows something that is missing in the individual, stationary 

billow simulation: the 2-D vortex strands or braids that connect the individual billows. These are 

thought to be an additional source of coherent turbulence. The time series of the velocity and 

turbulence parameters at y = 30 and z = 85 m for the simulated evolving, stationary K-H billow 

is plotted in Figure 7-3. The primary phases are indicated: the maximum 2-D structure, full 3-D 

turbulence, and the fully mixed or saturated state. Of particular interest are the bursts of Ecoh that 

are associated with the U velocity maxima or gusts during the billow breakdown. 

146
 
 

Figure 7-1(a). Maximum K-H billow 2-D structure at about t = 30 seconds, with secondary 

instabilities by t = 44 seconds and strong turbulence formation afterward 

147 
 

 

Figure 7-1(b). Fully 3-D turbulent flow by t = 70 seconds 

148 
 

Figure 7-1(c). Fully mixed flow (saturated) by t  170 seconds, with internal waves forming at 

upper and lower boundaries 

149 
 

150 

Source: Adapted from “Kelvin-Helmholtz Clouds” (DI00152) by Terry Robinson, copyright University Corporation 

for Atmospheric Research 

Figure 7-2. Cloud formation of evolving K-H billows. Flow and evolution are from right to left. 

2-D vortex 

braid Growing 

Initial 

Shear 

Layer 

Roll Over & 

Breakdown 

(Turbulence 

Phase) 
 

 

Figure 7-3. Time series of evolving stationary K-H billow at y = 30 and z = 85 m. The phases of the 

evolution—formation, turbulent breakdown, and fully mixed saturation—are indicated. 

151 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7.2 Turbine Dynamic Response to a Simulated K-H Billow

To understand the consequences of a turbine rotor ingesting a K-H billow, we interfaced the 

NCAR LES simulation into the NREL AeroDyn aerodynamics module and used the 

MSC.ADAMS multibody dynamics code to derive the resulting turbine dynamic response. We 

simulated the 1.5-MW baseline virtual turbine developed for the rotor study of the Wind 

Partnership for Advanced Component Technologies (WindPACT) Project by D.J. Malcolm and 

A.C. Hansen (2002). For more details see Section 8 of Kelley and colleagues (2004). 

The simulated K-H billow was scaled to encompass the entire 70-m rotor diameter of the 

WindPACT baseline turbine. The background hub-height mean wind speed was chosen to be 17 

m s–1, higher than the rated wind speed of 12 m s–1 

so that peak power was modulated by the 

control system. The shear exponent across the rotor was 0.578. The actual period of wave 

excitation of the turbine model was 271.7 seconds in scaled time. Figure 7-4 maps inflow to the 

turbine in terms of the x–z temperature field (equivalent to velocity streamlines) in which scaled 

time was adjusted so that t = 0 seconds corresponds to when the billow has achieved its 

maximum 2-D structure but with little turbulence. At t = 91.5 seconds turbulent breakdown has 

been initiated, at t = 166.2 seconds the flow is fully three-dimensionally turbulent, at t = 217.7 

seconds stabilization is beginning to take place, and finally at t = 271.7 seconds turbulent 

saturation has occurred and internal waves have formed at the upper and lower boundaries. 

Figure 7-5 plots the corresponding time series of the turbulence parameters. At the beginning of 

the turbulent breakdown, at about t = 97 seconds, at hub height there is a significant downward 

flux of horizontal momentum and turbulent kinetic energy, about half of which is coherent, as is 

shown in Figure 7-6a. This downward transport of momentum causes the hub-height wind speed 

to peak at about 17.8 m s–1. Figure 7-6b shows the same parameters between about t = 112 and 

146 seconds, when the turbulence has an energetic 3-D structure, which creates intense vertical 

mixing that decreases the shear, as shown in Figure 7-7. A short increase in the shear late in the 

record is related to the stabilization and the formation of internal gravity waves. 

We began the K-H billow inflow to the WindPACT AeroDyn/MSC.ADAMS simulation at the 

point when the billow had reached its maximum 3-D structure (at t = 0 in Figure 7-4). Initially 

we started the simulation at the beginning (ignoring the first 30 seconds to allow numerical 

startup transients to decay), but found that because there was little or no turbulence during the 

billow rollup (see Figure 7-a and the first 50 seconds of Figure 7-3) we observed a very passive 

dynamic response in the turbine; i.e., the turbine was dynamically insensitive to the rollup phase 

of the billow. By initializing the inflow at the point of billow rollover and breakdown (~ 70 

seconds into the simulation in Figure 7-3), we could examine the impact of the transition from 

the 2-D structure to the fully turbulent 3-D structure and then as it decayed to saturation as 

shown in Figure 7-5. 

152
 
Time Record 566

Time Record 2500

ime Record 4000

Time Record 5000

Time Record 6000

rotor 

plane 

z (m) 

100
 

80
 

60
 

100
 

80
 

60
 

100
 

80
 

60
 

100
 

80
 

60
 

100
 

80
 

60
 

-30 -20 -10 0 10 20 30 

-30 -20 -10 0 10 20 30 

-30 -20 -10 0 10 20 30 

T 

-30 -20 -10 0 10 20 30 

t = 0 s 

t = 

91.5 s 

t = 

166.2 s 

t = 

217.7 s 

t = 

271.7 s 

-30 -20 -10 0 10 20 30
 

x (m)
 

Figure 7-4. Evolution of K-H billow used as input to simulation of WindPACT 1.5-MW baseline 

turbine 

153
 
18 

UH 

17 

16 

15 

2 

1 

0 

u' -1 v' 

w'

-2
 

2
 

1 

0 

u'w' -1 u'v' 

v'w' 

-2 

2.5 

ET 2.0 E 

Ecoh 1.5 

1.0 

0.5 

0.0 

0 50 100 150 200 250 

Time (s) 

Figure 7-5. Time histories of hub-height UH, u’, v’, and w’, u’w’, u’ v’, and v’w’ and ET and Ecoh

input into WindPACT baseline turbine model

m2/s 2 m/s 

m2/s 2 m/s 

154
0 

18.0 1.0 2

(a) 

0.5 

17.5 1

0.0 

w'E, w'Ecoh (m 3/s 3) w'E, w'Ecoh (m3/s 3) 

17.0 

-0.5 

UH (m/s) 

UH (m/s) 

u'w' (m2/s 2) u'w' (m2/s 2) 

16.5 

-1.0 

UH
 

u'w'
 

-1 

16.0 

w'E -1.5 

w'Ecoh 

15.5 -2.0 -3

80 85 90 95 100 105 

Time (s) 

18.0 1.0 2

(b) 

0.5 

17.5 

1 

0.0 

17.0 

-0.5 

16.5 

-1.0 

0 

-1 

16.0 

-1.5 

15.5 -2.0 -2

115 120 125 130 135 140 145 

Time (s) 

Figure 7-6. Time histories of hub-height UH, and fluxes of momentum (shear stress) u’w’, ET, and 

Ecoh for two periods. Period (a) is characterized by the intense downward fluxes of momentum, 

total (ET), and coherent (Ecoh) turbulent kinetic energy as the K-H billow rolls over and breaks into 

fully 3-D motions. Period (b) is characterized by much smaller scale turbulent motions containing 

both positive and negative fluxes.

155

-2 
 

0.8 0.16 

Rotor layer mean shear exponent 0.7 0.14 

0.6 0.12 

Rotor layer mean shear (1/s) 

0.5 0.10 

0.4 0.08 

0.3 0.06 

0 20 40 60 80 100 120 140 160 180 200 220 240 260 

time (s) 

Figure 7-7. Decrease in rotor layer mean vertical shear during life cycle of simulated K-H billow

In Figure 7-8 we present time series graphs of the hub-height horizontal wind speed and 

Reynolds stress components and below that the turbine response in the form of the root out-ofplane or flapwise bending moment with the mean removed. In panel (a) we plot the continuous 

wavelet transform (CWT) scalogram of the root bend load. Frequency is inversely scaled 

nonlinearly on the ordinate and the intensity of the stress energy is indicated by the colors. Deep 

reds indicate the highest levels of stress and blue-black indicates minimal stress levels. This plot 

shows the distribution of stress energy levels as a function of frequency and time. The red oval 

indicates a period of high frequency response in the blade load. In panel (b) we plot time series 

of the load stress in kNm partitioned into six detail frequency bands, D4 through D9, by applying 

the discrete wavelet transform (DWT) to the loading signal. Table 7-1 lists the frequency ranges 

associated with these detail bands and their general modal characteristics. 

156
 

 

(b) 

(a) 

Figure 7-8. Wavelet analysis of dynamic response of WindPACT baseline turbine zero-mean root 

bending moment to simulated stationary K-H billow: (a) scalogram of decomposition by 

continuous wavelet transform—deep reds indicate high dynamic stress levels and dark blue low 

levels; (b) decomposition of root load time series with discrete wavelet transform. Bandwidths of 

the discrete wavelet transform frequency bands D4 through D9 are shown in Table 7-2. High 

frequency response in the root load time series is highlighted by the red oval. 

157 
 

Table 7-1. WindPACT Turbine Calculated Static System Frequencies 

Wavelet 

Detail Band 

Frequency 

Range (Hz) 

Characteristic 

Modes 

Total 

Number of 

Modes 

Number of 

Blade/Tower 

Interacting Modes 

D9 0.234–0.469 1-P, Tower bending 2 0 

D8 0.469–0.938 2-P 0 0 

D7 0.938–1.875 Blade 1st bending 3 0 

D6 1.875–3.75 Blade 2nd bending 5 2 

D5 3.75–7.5 Blade, blade/tower 3 1 

D4 7.5−15 Blade, blade/tower 7 5 

D3 15 −30 Blade, blade/tower 7 3 

Source: Adapted from Jonkman and Cotrell (2003) 

158
 
Table 7-2. Calculated WindPACT Baseline Turbine System Nonrotating Modal Frequencies 

Nominal 

Modal 

Frequency (Hz) 

Mode Shape Descriptions Indicated 

Rotor/Tower 

Coupling 

Wavelet 

Detail 

Bands Primary Mode Secondary Couplings 

0.407 Tower 1st lateral bending D9 0.408 Tower 1st fore-aft bending 

1.153 Blade 1st asymmetric flap 

D7 

1.205 Blade 1st asymmetric flap 

1.258 Blade 1st symmetric flap 

1.608 Blade 1st symmetric edge 

1.842 Blade 1st asymmetric edge 

1.870 Blade 1st asymmetric edge 

2.912 Blade 1st flap, tower fore-aft 

bending 

3.270 D6 Blade flap, edge, & tower foreaft bending 

3.661 Blade 2nd asymmetric flap 

3.748 Blade 2nd symmetric flap 

5.568 Blade 2nd symmetric edge 

6.009 D5 Blade flap, edge, & tower foreaft bending 

6.125 Blade 2nd symmetric edge 

8.143 Blade 2nd edge asymmetric Tower 2nd lateral, blade tips 

in-plane bending 



D4 

10.190 Blade 2nd flap asymmetric Blade tips in-plane tip bending, 

tower 2nd fore-aft bending 

12.614 Blade tips in-plane bending, 

tower 2nd lateral bending 

13.541 Asymmetric flap, tower fore-aft 

bending 



14.113 Blade symmetric flap, 

asymmetric edge 

14.122 Asymmetric flap, asymmetric 

edge, tower fore-aft 

14.215 Asymmetric flap, asymmetric 

edge 

15.005 Asymmetric flap, asymmetric 

edge 

D3 

15.315 Symmetric flap, tower lateral, 

collective lag 

16.022 

16.487 

Asymmetric flap, blade torsion, 

tower fore-aft 

Blade torsion 



16.510 Blade torsion 

16.528 Blade torsion, slight tower 

fore-aft 

20.407 Asymmetric flap 

159
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Kelley and coauthors (2000) give a more complete discussion of wavelet analysis as we applied 

it to assessing wind turbine dynamics. Table 7-2 summarizes the nonrotating modal or natural 

frequencies for the WindPACT virtual turbine determined from a study of the model with the 

ADAMS /Linear eigenvalue analysis program. 

The deep red areas in Figure 7-8a beginning at the left and continuing to about t = 100 seconds 

correspond to the tower bending and blade first flapwise bending modes listed in Table 7-2 that 

are being driven by the significant vertical wind shear shown in Figure 7-7. The time history 

variations in the tower bending and first blade symmetric and asymmetric bending loads can be 

seen in Figure 7-8b in the D8, D9, and D7 detail bands, respectively. The rapid decrease in level 

of these loads starting at about t = 180 seconds corresponds to the significant decrease in the 

vertical shear across the rotor shown in Figure 7-7 as a consequence of the intense mixing that 

accompanied the billow breakdown into intense 3-D turbulence. 

The billow rollover and breakdown begin at about t = 135 seconds and continue until about t = 

180 seconds. The highlighted area of Figure 7-8 of the panel containing the out-of-plane moment 

loading history shows the presence of much higher frequency components, particularly from 

about t = 140 to 180 seconds. During the period, as the turbulence become 3-D and contains 

coherent elements, loading bursts can be seen in the higher frequency D4, D5, and D6 detail 

bands. According to Table 7-2, this frequency range contains a significant amount of secondary 

or cross-coupling of modes (stress energy fluxes). From Figure 7-6b, the rotor inflow at this time 

is filled with energetic turbulent structures that have dimensions much less than the rotor 

diameter, and it is these smaller structures that are contributing to the excitation of these higher 

order modes. As the turbulence in the decaying billow begins to saturate at about t = 200 

seconds, the modal excitation also decreases in both occurrence and intensity as a more stable 

temperature gradient (increasing Ri) begins to reestablish itself and the accompanying increase in 

buoyancy damping limits the growth rate and size of the turbulent eddies. This is demonstrated 

in Figure 6-14. 

The role of coherent TKE, or Ecoh, can be seen a bit more clearly in Figure 7-9. Here the format 

of Figure 7-8 has been modified to better describe the process. The three top panels contain rotor 

disk (y-z) contour plots for the indicated time period of (left) the vertical velocity field with 

darker shades of red and blue depicting higher values of rising and descending air, respectively; 

(center) regions of Ecoh with the dark red signifying the more intense; and (right) the total wind 

speed (the vector sum of horizontal and vertical components) with deep red the greatest speed 

and dark blue the lowest speed. An idealized facsimile of the WindPACT turbine is 

superimposed on each of the panels with the blade root bending load measurements depicted in 

the time series and the CWT scalogram and DWT detail band time-frequency decompositions 

from it. The upper center panel shows that the coherent structures in this record are much smaller 

than the rotor disk in this highly turbulent flow as revealed by the left and right panels. The 

higher frequency content in the load time history is evident by the significant deviation from a 

sine wave shape that would be expected from the load variation from vertical wind shear alone. 

This deviation arises from the blade passing through this highly turbulent field (left and right 

panels) that contains coherent structural elements (center panel). The red vertical dot-dashed 

lines highlight the dynamic response transients across a wide frequency range to coherent 

structural elements encountered by the blade in the inflow. These represent coherent stress 

responses across the frequency range of 1.875 to at least 20.4 Hz, the highest modal frequency 

160
 
listed in Table 7-2, which resides within the D3 (15 to 30 Hz) detail frequency band. This is in 

the modal frequency range where the contents of this table show that numerous cross-couplings 

exist between tower and blade modes and, though not determined, the drivetrain as well. These 

represent potential paths for the transfer or flux of stress energy to various parts of the turbine. 

This can be summed up by pointing out that a coherent excitation (from coherent turbulence) 

elicits a coherent dynamic response in the turbine. 

161
 
Figure 7-9. Continuous and discrete wavelet decompositions of root flapwise bending load 

induced in WindPACT turbine model from LES K-H billow simulation. The time history of the blade 

root flapwise bending load with the mean removed is plotted in the second panel from the top. 

The dot-dashed vertical lines mark coherent responses across a frequency range of 1.875 to 30 Hz 

as a result of the blade marked with the dashes encountering the coherent structures in the center 

top panel. 

162 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

7.3 Flux of Coherent Turbulent Energy into Turbine Structures

Clearly the character of the waveforms in Figure 7-9 changes with the frequency ranges or, 

equivalently, the center frequencies of the detail bands rise. In Bands D6, D5, D4, and D3, the 

waveforms increasingly take on the characteristic of transient damped oscillations whose lengths 

become shorter as both the frequency bandwidth and center frequency of the bands increase. 

This indicates that the loads within these frequency bands are being applied more as an impulse 

as opposed to a load variation that is occurring over one blade revolution (1-P), i.e., in Band D9 

and at the twice per revolution (2-P) rate in Band D8. As the peak amplitudes of the load time 

histories in Bands D6 through D7 decrease, the number of stress reversals increases as the rotor 

passes through coherent turbulent structures. Because of the nature of the load application and 

the existence of the small values of structural damping seen in most large turbines, it is likely 

that there is a significant transient storage of vibrational energy that must be dissipated. It also 

seems likely that, under these circumstances, the possibility of modal dynamic amplification may 

also exist, which could be a contributing factor in the lower than designed component service 

lifetimes being seen in operating wind farms. 

The sources of these brief transient loads depicted in the higher frequency detail bands in Figure 

7-9 are the coherent turbulent structures through which the rotor blades pass. In the work of 

Kelley and coauthors (2000), and previously in this report, we demonstrated using wavelet 

analysis tools that a blade encountering a coherent turbulent structure induces transient loads that 

couple energy into the rotor natural vibration (modal) frequencies. We demonstrate this process 

in which we examine the nonstationary time and frequency transport or flux of coherent 

turbulent energy Ecoh from the velocity field to the rotor blade manifested as variations in the 

blade dynamic pressure or qc at a given spanwise location. We use the wavelet technique of the 

coscalogram as applied by Gurley and Kareem (1999). The coscalogram, as used in this context, 

maps the time-frequency variation of the energy flux from the excitation (Ecoh) to the response 

(qc) variable. It is analogous in many respects to Fourier cross-spectral analysis but with the 

variation in spectral energy resolved not only in frequency but also in time. 

We excited the WindPACT turbine model with the breaking portion of the LES K-H billow and 

obtained the individual time series Ecoh of the blade dynamic pressure at the 78% span element 

and the velocity field in the inflow at that location. The coscalogram of these two variables 

represents the response of qc to the Ecoh excitation or the energy flux from the coherent velocity 

field to the blade as manifested by the time variation of qc. The fluctuating dynamic pressure 

excites the blade modal frequencies, many of which are lightly damped. This results in the 

storing and propagation of vibrational energy within the remainder of the turbine structure. 

In Figure 7-10 we demonstrate this flux transfer process. Here we plot the interaction between 

the local Ecoh presented to the blade and the resulting qc at the 78% blade span station for the 

modeled WindPACT rotor. The upper panel displays the time series of the Ecoh in red and the qc 

in blue. The time-frequency variations of the energy content of each of these variables are shown 

in the two panels immediately below, and variation of the energy transport or flux between Ecoh 

and qc is displayed in the lowermost panel. In this short record, the 78% blade span station 

encounters an intense region of Ecoh, with a peak value approaching 40 m2 s

–2 at a time between 

25 and 30 seconds into the record. Although the most intense flux of energy (dark red in 

lowermost panel) from the coherent turbulence to the blade is found in the lowest 

163
 
 Local E coh Excitation (m2 /s2 ) 2 Local Dynamic Pressure, q c Response (Pa)2 Local Relative Energy Flux (m2 /s2 Pa) Local E coh (m2 /s2 ) 

Local Dynam c i

Pressure, q c 

P( a) 

Frequency Frequency Frequency 

Time (s) 

Figure 7-10. Spectral flux of coherent turbulent energy from NCAR LES simulated K-H 

billow into WindPACT rotor blade at 78% blade span station 

164 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

frequencies, transfers also occur at the higher frequency vibrational modes in Table 7-2 (greater 

than ~ 3 Hz). These are somewhat difficult to see because of the nonlinearity of the frequency 

axis. This process can be described as a resonant coupling between the spatiotemporal structures 

in the coherent turbulent inflow field and vibrations created within the blade structure as a result 

of the lightly damped structural modes. We believe this explains the 1:1 correspondence 

observed in the spectral frequencies of the coherent turbulence field and the vibratory response 

of the turbine blades, discussed in Kelley and coworkers (2000) and illustrated in Figure 7-10. 

The spatiotemporal characteristics of the turbine inflow turbulence field are very important in 

determining not only the aeroelastic response of the blades but also the rate and intensity at 

which turbulent energy is transferred from the turbulence to the rotor and subsequent structure. 

To demonstrate this we again use the virtual WindPACT turbine model by exciting it with 

TurbSim simulated inflow turbulence fields generated using a mean hub-height wind speed of 13 

m s

–1: (1) in accordance with the specifications of the IEC Kaimal Normal Turbulence Model 

(NTM; TurbSim IECKAI spectral model) for “A”-level turbulence and the Normal Wind Profile 

(vertical shear exponent of 0.2; IEC 2005) ; (2) a stable flow above flat, homogenous terrain 

based on the models of Højstrup (1982) and Olesen and coauthors (1984) implemented in 

TurbSim as the smooth terrain (SMOOTH) spectral model with an intense vertical shear 

exponent of 1.49 but no added small-scale coherent turbulent structures; and (3) the breakdown 

of the NCAR LES simulated K-H billow with an initial shear exponent of 1.49 (the shear 

decreases during the breakdown because of the intense vertical mixing that takes place as shown 

in Figure 7-7). 

In Figure 7-11 we compare the energy flux from coherent turbulence to the blade dynamic 

pressure at the 78% span station of the WindPACT turbine model for the three inflows defined 

previously. Here we present the information shown in the lowermost panel of Figure 7-10 but in 

a 3-D format with the magnitude of the energy flux logarithmically scaled by height on the 

vertical axis and not as shades of red and blue. Examining the three graphs reveals that at least an 

order of magnitude greater energy flux up to the highest frequencies with the breaking K-H 

billow in the inflow (Figure 7-11c) as compared with the IEC Kaimal NTM (Figure 7-11a) and 

highly sheared stable flow (TurbSim SMOOTH model) (Figure 7-11b). The IEC Kaimal NTM 

inflow transfers a smaller but significant energy flow into the turbine rotor up to about 3–4 Hz 

but then decreases rapidly at higher frequencies in comparison with the K-H billow breakdown 

and its intense, small-scale coherent structures. The stable, highly sheared flow (Figure 7-11b) 

creates similar levels of energy flux as the K-H billow at the lowest frequencies because of the 

strong wind shear. The flux then decreases rapidly with increasing frequency as a consequence 

of the lack of coherent turbulent structures. These three diagrams illustrate, at least in terms of 

the flux of energy from the turbulent inflow into the turbine rotor blades, that the character and 

structure of the inflow are very important in determining turbine structural response. 

In Figure 7-12 we apply the wavelet coscalogram to examine the relative energy flux from the 

coherent turbulent kinetic energy Ecoh to the local dynamic pressure qc at the 78% blade span 

station for the WindPACT virtual turbine using the IEC Kaimal NTM spectral model for the 

inflow. We increased the hub-height mean wind speed to the above-rated value of 16 m s–1 but 

maintained the “A” turbulence level and the NWP shear exponent of 0.2. Immediately obvious is 

the significant tower bending response at ~ 0.4 Hz, as indicated by the modal mapping in Table 

4-3. The tower appears to respond to one distinct coherent structure response at about 12 seconds 

165
 
 

 

 

 

 

 

 

 

into the record. As in Figure 7-11a, above about 6–7 Hz the response falls rapidly, with no 

indication of reactions to coherent turbulent structures of any consequence. 

In Figures 7-13 and 7-14 we also increased the hub-height mean wind speed to the same value 

for the smooth terrain (TurbSim SMOOTH spectral model) and the NCAR LES K-H billow 

inflow simulations. We added an inflow simulation shown in Figure 7-15 of a K-H billow 

derived from the Werne and Fritts (1999) Colorado Research Associates (CoRA) DNS model to 

obtain another coherent structure sequence. We increased the rotor disk shear exponent from 

1.49 to 1.825 for all three simulations to increase the intensity of the coherent structures. Late in 

the record, between about 53 and 67 seconds of the SMOOTH spectral model inflow simulation 

in Figure 7-13, are significant responses in the lowest frequency mode shapes to coherent 

turbulence fluxes, but this response falls off rapidly with increasing frequency, indicating a lack 

of smaller scale coherent structures in the flow. Comparing the SMOOTH modeled inflow 

response to the NCAR LES and CoRA DNS K-H billows in Figures 7-14 and 7-15, we see 

slopes in the high frequency responses, but they are much shallower. This shallower slope 

coincides with a significant amount of modal cross-coupling in Table 7-3. At 10 Hz is almost an 

order of magnitude more coherent turbulent energy flux, which the time series of qc reflect. In 

both K-H billow inflow simulations are two events with significant fluxes that affect the modal 

frequencies greater than 10 Hz, as indicated by the dashed lines. The presence of intense, 

coherent turbulent structures in the breakdown phase of a K-H billow clearly is an important 

source of kinetic energy influx into a turbine rotor blade, particularly for the higher frequency 

mode shapes where numerous cross-couplings exist. 

166
 
) 

IEC NTM EXCITATION 

SLIGHTLY STABLE FLOW WITH HIGH VERTICAL SHEAR EXCITATION 

BREAKING KH BILLOW EXCITATION 

Frequency (Hz

Time (s) 

Relative Energy F ul x m( 2 /s 2 P- a) Relative Energy F ul x m ( 2 /s 2 -Pa) Relative Energy F ul x m ( 2 /s 2 -Pa) 

Time (s) 

Time (s) 

Frequency (Hz) 

Frequency (Hz) 

(b) 

(c) 

(a) 

Figure 7-11. Relative spectral energy flux (coscalogram) of Ecoh to blade dynamic pressure 

(qc ) at 78% span for simulated inflows of (a) IEC Kaimal NTM; (b) stable flow with high 

shear (SMOOTH spectral model); and (c) breaking NCAR LES K-H billow 

167 
 

 

Figure 7-12. Relative energy flux coscalogram between Ecoh and qc at simulated WindPACT turbine 

78% span station for inflow from IEC Kaimal NTM spectral model simulation 

Figure 7-13. Relative energy flux coscalogram between Ecoh and qc at simulated WindPACT turbine 

78% span station for inflow from high shear SMOOTH model simulation. Low-amplitude energy 

flux indicated with dashed lines is associated with frequencies greater than 10 Hz. 

168 
Figure 7-14. Relative energy flux coscalogram between Ecoh and qc at simulated WindPACT turbine 

78% span station for inflow from NCAR LES K-H billow simulation. Significant energy flux 

indicated with dashed lines is associated with frequencies greater than 10 Hz. 

Figure 7-15. Relative energy flux coscalogram between Ecoh and qc at simulated WindPACT turbine 

78% span station for inflow from CoRA DNS K-H billow simulation. Significant energy flux 

indicated with dashed lines is associated with frequencies greater than 10 Hz. 

169 
 

 

 

 

 

 

 

 

 

 

 

 

7.4 Propagation of Coherent Turbulent Energy into Turbine Structure

In analyzing the response of the WindPACT turbine to coherent turbulence, we are limited 

because it is a virtual machine and the details of the modeling were limited. For example, the 

drivetrain was not included in the linear modal analysis. As a result we were not able to perform 

more detailed analyses of the load path dynamics downstream of the rotor as it responds to 

coherent turbulence excitation. In the LIST Program using the NWTC ART, however, we can 

look deeper into such questions because of the extensive documentation and measurements 

available. 

A full system modal test was included in developing the dynamics model of the controls test bed 

turbine (CART2), and it was performed on another original Westinghouse machine identical to 

the ART. Osgood and colleagues (2002) performed a full system modal survey that included a 

“snap back” transient load test (Osgood 2004) and estimates of modal damping. Wright (2004) 

developed the MSC.ADAMS model of CART2 (ART), which we used to perform an 

ADAMS/Linear modal analysis. We were then able to compare these results to those derived 

from Osgood’s full system modal survey. Table 7-3 summarizes these results, and the modal 

frequencies where we found significant numbers of cross-couplings are shaded and bolded. Of 

particular importance is the inclusion of the drivetrain modes. A significant number of crosscoupled modes appear above about 3.8 Hz, some of which are very lightly damped. The upper 

frequency limit of the measured modal survey was slightly more than 6 Hz, so we have to 

depend on the eigenvalue analysis of Wright’s MSC.ADAMS model for high frequencies. 

Table 7-4 gives a detailed summary of the measured modal survey combined with the eigenvalue 

analysis. Modal frequencies with cross-coupling between the rotor and tower or drivetrain are 

highlighted. In general, there was reasonable agreement between the measured and the calculated 

modal frequencies where available, with the former showing more potential load paths. Of 

particular significance were the modal damping estimates within these cross-coupled frequency 

ranges, some of which were quite small and not available from the linear analysis. Of particular 

note are the number of cross-coupled modes among the rotor blades, the tower, and the drivetrain 

and the low modal damping associated with the majority of them. So with the ART, although 

smaller, we have a good picture of the modal dynamics that we lacked with the virtual 

WindPACT turbine. 

We can now examine the details of the flux of coherent turbulent energy into the ART based on 

actual measurements. We use the loading transients created by the rotor blades encountering an 

intense coherent turbulent structure (CTKE) in the upper panel of Figure 7-16. The zero-mean 

root flapwise bending load response to this structure is plotted in the center panel. The fore-aft 

(X), side-to-side or lateral (Y), and vertical (Z) velocities measured by a triad of orthogonal 

accelerometers of an inertial measurement unit (IMU) attached to the top of the forward lowspeed shaft bearing or pillow blocks are presented in the bottom panel. Before the intense 

transient event, the velocities (particularly those in the fore-aft direction) were reasonably high 

because of the high levels of coherent turbulence occurring in the inflow. 

In Figure 7-17, we illustrate the observed time-frequency variation of the propagation or flux or 

vibrational energy between the ART root bending loads and the low-speed shaft during the 

rotor’s encounter with the intense coherent turbulent structure indicated in the upper panel of 

Figure 7-16. In these presentations we plot the time series of the zero-mean root flapwise 

170
 
 

 

 

 

 

 

 

 

 

 

 

bending load in red together with the fore-aft, side-to-side, and vertical nacelle velocities in blue 

and the low-speed shaft torque (blue) and flapwise bending (red) in the rightmost panel in Figure 

7-17a. Figure 7-17b is the same, with the edgewise bending load replacing the flapwise load. In 

the second row of panels below the time series plots are the CWT scalograms of the excitation 

flap and edge bending loads. CWT scalograms of the nacelle X, Y, and Z velocities and the lowspeed shaft torque are presented in the second row of panels. Finally, in the lowest row of panels 

are coscalograms indicating the energy fluxes of the excitation loads with the responses of the 

IMU velocity components and the low-speed shaft torque. In this presentation the coscalogram 

allows us to examine and quantify the time variation of the intensity and frequency content of the 

flow of vibrational energy as the blades pass through the coherent turbulent structure. 

From Figure 7-16, we note that the impact of this encounter was applied over a period of about 2 

seconds, but we cannot ascertain what the spectral content of the energy flow between the blade 

roots and the low-speed shaft is and what modal frequencies may be involved. The impulsive 

nature of this event is well demonstrated in Figure 7-17. With the exception of the side-to-side Y 

nacelle velocity, the coscalograms show that energy is flowing across a wide or broadband 

frequency range that is consistent with the application of a short-period, impulsive load. By 

comparison, the side-to-side or lateral energy flow resides within a narrowband range of 

frequencies near 6 Hz. According to Tables 7-3 and 7-4, this is a range dominated by numerous 

lightly damped and cross-coupled modes among the blades, the tower, and the drivetrain. 

Therefore vibrational energy that originates with the coherent turbulent structure is responsible 

for inducing unsteady aerodynamic loading of the blades. The resulting dynamic loads are 

transported throughout the blades and tower and into the low-speed shaft and nacelle in an 

impulsive manner. Even though this experiment did not directly measure tower loads, we would 

expect responses similar to those in Figure 7-17. The impulsive loading of turbine rotors by 

coherent turbulent structures is responsible for the transport of vibrational energy into turbine 

components through the action of lightly damped modes and, in particular, cross-coupled modes. 

7.5 Extension to Larger Turbine Rotors

In comparing the detailed modal mapping of the ART in Table 7-4 with that of the larger 

WindPACT design derived from linear analysis alone in Table 7-2, we see that many of the 

cross-coupled modes nominally occur in the same frequency ranges, i.e., 3–9 Hz. Even though 

the detail available in the ART modal mapping does not exist for the virtual WindPACT turbine, 

it is clear from Table 7-2 that the frequency range of the cross-coupled modes seen in the blades 

and tower extends to about twice that of the ART. We have no estimate of the modal damping 

associated with these higher frequencies, but it is likely that at least some of them are equivalent 

to the low values seen in the ART. We would also expect, as in the ART, modal cross-coupling 

among the blades, tower, and drivetrain components. An increase from a 600-kW turbine with a 

42-m-diameter rotor to a 1,500-kW turbine with a 70.5-m-diameter rotor leads to additional and 

higher frequency cross-coupling modes, most likely because of the unavoidable increase in 

flexibility with the larger turbine design. 

To test this theory, we used the ADAMS/Linear program to analyze the linear mode shapes of 

the virtual NREL 5-MW Reference Turbine (Jonkman and Cotrell 2003). Using the animation 

graphic tool of ADAMS/Linear, we swept the model design over the excitation frequency range 

of 0.01 to 20 Hz in very small increments while paying close 

171
 
 

Table 7-3. CART2 (ART) Measured and Calculated Static System Frequencies 

Frequency 

Range (Hz) 

Characteristic 

Modes 

Range of 

Measured 

% Critical 

Damping 

Total 

Number of 

Modesa 

Number of 

Blade/Tower/ 

Drivetrain 

Interacting 

Modesa 

0.716 1-P ~ ~ ~ 

0.867–0.886 

Blade 1st bending, tower 

1st fore-aft bending, 

drivetrain bending 

0.68–2.66 7 3 

1.390–1.580 

Blade 1st bending, tower 

side-side bending, drivetrain 

lateral bending 

0.74–1.52 3 2 

2.060–2.081 Blade 1st & 2nd bending 0.70–0.93 3 0 

3.886–4.451 

Blade 1st & 2nd bending, 

drivetrain lateral bending, 

tower torsion 

0.70–0.72 6 7 

5.050–6.170 Blade bending, drivetrain, 

tower lateral & torsion 0.24–0.95 8 10 

7.815b

–8.411b 

Blade bending, tower 

fore-aft & lateral bending, 

drivetrain bending 

n.ac 

2 3 

9.305b

–10.84b Blade bending, drivetrain 

interaction n.a. 2 1 

a

Measured plus modes from FAST model eigenanalysis

b

Determined from FAST model eigenanalysis only c

Not available 

Sources: Osgood, McFarland, and Johnson (2002); Osgood (2004); Wright (2004) 

172
 
 

 

 

 

 

 

 

 

 

 

 

 

Table 7-4. CART2 (ART) System Nonrotating Modal Frequencies 

Natural Frequency (Hz) Measured 

% Critical 

Damping 

Mode Shape Descriptions Indicated Coupling 

Measured# 

Eigenvalue 

Analysis§ Primary Mode Secondary Couplings Rotor/ 

Tower Blades Drivetrain 

Horiz 

Blades 

Vert 

0.0130§ Hub teetering Blade 1st & 2nd symmetric flap 

0.867 2.660 Tower 1st lateral bending 

0.858 0.661 Tower 1st fore-aft bending 

0.878 Tower 1st fore-aft bending Blade 1st symm flap; 1st asym edge; tower 1st fore-aft bending; drivetrain  

0.870 0.683 Tower 1st fore-aft bending 

0.877 1.800 Tower 1st lateral bending 

0.866 Tower 1st fore-aft bending Blade 1st symm flap; 1st symm edge, 2nd symm flap; tower 1st lateral bending 

1.390 Blade 1st symma flap Drivetrain; tower 1st lateral; blade 2nd symm flap 

1.45 0.743 Blade 1st asymb edge; tower lateral bending & 

torsion 

1.58 1.520 Blade 1st asym flap 

2.06 0.698 Blade 1st symm flap Blade 1st asymmetric edge 

2.06 0.927 Blade 1st symm flap 

2.081 Blade 1st symm flap Blade 1st symm edge; 2nd symmetric flap 

3.886 Blade 1st asym flap Blade 1st asym edge; 2nd asym flap; teeter 

3.90 0.708 Blade 2nd asym flap Blade 1st symm edge; drivetrain lateral bending; tower torsion  

3.94 0.717 Blade 1st symm edge Blade 2nd asym flap; tower torsion 

4.02 0.710 Blade 1st asym edge Blade 2nd asym flap; drivetrain lateral bending; tower torsion  

4.09 0.695 Blade 2nd asym flap Blade 1st symm edge; drivetrain yaw; tower lateral & torsion  

4.451 Blade 1st asym edge Blade 1st & 2nd asym flap 

5.05 0.951 Blade 1st symm edge; 2nd asym flap; drivetrain yaw; tower lateral & torsion  

5.35 0.627 Blade 2nd symm flap; 1st asym edge 

5.39 0.584 Blade 2nd symm flap; 1st asym edge 

5.67 0.569 Blade 1st symm edge; 2nd symm flap; drivetrain pitch & lateral; tower fore-aft, lateral, & 

torsion  

5.77 0.235 Blade 1st symm edge; 2nd asym flap; drivetrain pitch & lateral; tower fore-aft; lateral, & torsion  

6.01 0.668 Blade 2nd asym flap; 1st symm edge; drivetrain; tower 2nd lateral bending; tower torsion  

5.854 Blade 2nd symm flap Blade 1st symm flap; 1st symm edge 

6.17 0.380 Blade 2nd asym flap; 1st symm edge; drivetrain pitch; tower fore-aft bending  

7.815 Blade 2nd asym flap Blade 1st asym flap; 1st asym edge; tower 1st fore-aft bending 

8.411 Blade 1st symm edge Blade 1st & 2nd symm flap; tower 1st & 2nd lateral; drivetrain  

9.305 Blade 1st & 2nd asym flap 

10.837 Blade 1st symm edge; 1st & 2nd symm flap; drivetrain 

a

Symmetric b

Asymmetric 

Sources: Osgood, McFarland, and Johnson (2002); Osgood (2004); Wright (2004) 

173
 
rotor top (58m) 120 120 rotor hub (37m) Upwind array rotor left (37m) inflow CTKE 100 rotor right (37m) 100 

rotor bottom (15m) 

80 80 

60 60 

40 40 

20 20 

0 0 

400 400 

300 300 

Blade 1 

200 Blade 2 200 

100 100 

0 0 

-100 -100 

zero-mean -200 -200 root flap 

-300 bending -300 

moment 

-400 -400 

20 vertical (Z) 20 

side-to-side (Y) 

fore-aft (X) 

10 10 

0 0 

-10 -10 

-20 -20 

IMU velocity components 

0 2 4 6 8 10 12 

492 494 496 498 500 502 504 

Time (s) 

Figure 7-16. Coherent turbulence induced severe transient loading event 

measured on NWTC ART during LIST Project by blade zero-mean root 

loads and nacelle velocities measured on forward low-speed shaft support 

bearing

mm/s kNm 

m2/s 2 

174
 

(a) 

(b) 

Figure 7-17. Observed energy propagation caused by coherent turbulent event excitation between 

low-speed shaft torque and (a) out-of-plane and (b) in-plane root bending loads and nacelle 

velocities measured on forward low-speed shaft support bearing immediately behind rotor 

175 
 

 

 

 

 

 

 

attention to locating and identifying cross-coupled modes. Table 7-5 summarizes the 52 mode 

shapes we found. We realize that not all of these listed will participate. From our experience with 

the measured modal survey of the CART2, however, it is also likely that mode shapes not on this 

list would exist on an actual, physical turbine. Also, some of them would undoubtedly be related 

to strongly nonlinear processes not resolved by ADAMS/Linear. We highlighted the crosscoupled modes for greater visibility and ease of comparison with the CART2 and the 

WindPACT turbines. Table 7-5 indicates that there is more potential cross-coupling below, 

within, and above the frequencies seen on the CART2 and the WindPACT turbines. At 

frequencies greater than about 10 Hz, the potential exists for complex, higher order modal 

coupling within the blades themselves and between the blades and the tower. What modal 

damping is associated with such interactions is unknown. Again, the drivetrain was not available 

in this model, so we do not know how the blades and the tower interact with it, but given the 

CART2 experience, it surely exists. These results suggest that as the turbine rotors and their 

towers increase in size, the increase in flexibility creates pathways for vibrational energy transfer 

throughout these components, which may be critical in terms of local fatigue damage when 

coherent turbulence is encountered during operations. 

176
 
Table 7-5. NREL 5-MW Reference Turbine Nonrotating System Modal Frequencies 

Nominal 

Modal 

Frequency (Hz) 

Mode Shape Descriptions Indicated 

Rotor/Tower

Coupling Primary Mode Secondary Couplings 

0.2017 Max rotor rotation rate (1-P) n.a. 

0.3162 1st tower lateral (side-to-side) bending 

0.3193 1st tower fore-aft bending 

0.6110 1st drivetrain bending 

0.6384 1st blade asymmetric Nacelle yaw 

0.6690 1st blade asymmetric Nacelle pitch 

0.7023 1st blade collective symmetric flap 

1.0751 1st blade asymmetric with edgewise pitch 

1.0744 1st blade asymmetric with flapwise yaw 

1.0886 1st blade asymmetric with edgewise yaw 

1.8576 2nd blade asymmetric with flapwise pitch 

1.9618 2nd blade collective symmetric flap 

2.6549 2nd blade collective edgewise 1st tower lateral 

2.8452 2nd tower fore-aft 2nd blade asymmetric 

2.9427 2nd tower lateral 2nd blade flap and edge 

3.0216 1st flapwise asymmetric blades 2 & 3 

3.9586 1st edgewise asymmetric blades 2 & 3 

4.0278 2nd blade flapwise and edgewise asymmetric 

4.0412 2nd blade flapwise and edgewise asymmetric Tower 1st fore-aft 

4.4685 1st torsion blade tips Tower 1st fore-aft 

4.9650 Complex interaction blade tips & nacelle yaw 

6.6997 2nd blade edgewise asymmetric collective 

7.0510 2nd blade flapwise & torsion 2nd tower fore-aft 

7.2607 2nd blade torsion 2nd tower lateral 

7.7588 1st blade collective torsion 

7.7781 1st torsion blade 1, 1st edgewise blades 2 & 3 

7.8609 1st torsion blades 2 & 3 

7.9732 1st torsion blades 1 & 3 

8.1035 1st blade collective torsion 

8.1736 1st torsion and 1st flapwise blades 2 & 3 

8.2865 2nd blade collective torsion 2nd tower fore-aft 

9.2865 2nd blade collective asymmetric edgewise 2nd tower fore-aft 

9.3381 2nd blade collective asymmetric edgewise 

11.7076 2nd flapwise asym blade 1, 2nd torsion blades 2 & 3 2nd tower fore-aft 

11.7215 3rd blade collective asymmetric flapwise 2nd tower fore-aft 

11.8544 3rd blade collective symm flapwise & 2nd torsion 

11.8902 3rd flapwise & 2nd torsion blades 2 & 3 

11.9246 3rd blade collective flapwise and 2nd torsion 

12.3317 3rd flapwise and 2nd torsion blades 2 & 3 

12.9411 3rd blade collective torsion 3rd tower lateral 

12.9972 3rd torsion blades 1 & 3 

13.0147 3rd blade collective torsion 3rd tower lateral 

13.0758 3rd blade collective torsion 3rd tower lateral 

13.2910 3rd blade collective torsion 3rd tower lateral 

14.2462 3rd blade collective asymmetric flapwise 3rd tower fore-aft 

16.3927 3rd blade collective asymmetric edgewise 

16.5404 3rd symmetric edgewise blades 2 & 3 3rd tower fore-aft 

16.5876 3rd asymmetric edgewise blades 1 & 3 

17.3138 4th blade collective symmetric flapwise 

17.3383 4th symmetric flapwise blade 1, 1st torsion blades 2 & 3 3rd tower fore-aft 

19.8192 3rd blade collective torsion 

19.8306 3rd blade collective torsion 3rd tower fore-aft 

19.8372 3rd torsion blades 1 & 2 

Source: Jonkman et al. (2009) 

177 
 

 

 

 

 

 

 

 

 

 

 

 

 

7.6 Modeling Coherent Turbulent Structures

Ingesting a coherent turbulent structure generated within the background flow as the result of 

Kelvin-Helmholtz Instability (KHI) can induce significant dynamic response in wind turbine 

structures. Such a response includes increased fatigue damage on the blades themselves through 

the direct application of cyclic stress loads or as vibratory energy that is transported from the 

blades impulsively through the drivetrain and into the tower. We have seen that the latter can be 

transported through the mechanism of lightly damped, cross-modal coupling. The coherent 

nature of K-H billows generates a range of stress loads at discrete frequencies when the blade 

passes through them, which in turn create an impulsive, coherent structural response in the 

turbine components. We need to develop a suitable engineering model of these turbulent 

coherent structures that can be scaled in terms of atmospheric boundary layer turbulence 

parameters. 

We analyzed the instantaneous time series of coherent kinetic energy (Ecoh) derived from a sonic 

anemometer for each usable 10-minute record at hub height (23 m) from the experiment in the 

California wind farm upwind of Row 1, upwind of Row 37 (the location of the two Micon test 

turbines with 7D upwind spacing), and downwind of Row 41 (14D downwind of the next 

operating row of turbines). Similarly, we analyzed the 7,041 10-minute records available from 

each of the five sonic anemometers in the upwind planar array of the NWTC LIST Program. 

Finally, the same process was applied to more than 28,000 10-minute records from the four sonic 

anemometers installed on the 120-m meteorological tower used as part of the Lamar Low-Level 

Jet Project (LLLJP) in the high plains of southeastern Colorado. 

Our initial analysis revealed that the number and intensity of coherent structures found within a 

10-minute record were exponentially distributed. Our further analysis found that these 

distributions could be reasonably described by an inhomogeneous Poisson random process. 

A Poisson process is a counting process in which N = {N(t), t ≥ 0 } refers to the number of 

events occurring in the interval (0, t ]. The probability of n events occurring in (0, t] is 

(λt )

n 

−λt P Nt { } () = n = e n = 0, 1, 2, ... , (7-2) 

n! 

where λ is the intensity or rate of occurrence. If λ > 0 and has a constant value, the process is 

referred to as homogeneous Poisson. If, however, λ is a function of time or other variables that 

are a function of time, the process is considered inhomogeneous Poisson. It is assumed that N(0) 

= 0; that it is stationary and events can be considered independent of one another; and that two 

events cannot occur simultaneously within a very small increment of time. If Sn is the time of the 

arrival of the nth event with So = 0, the time between events or interarrival time Xn is given by Sn 

– Sn-1 or 

n 

Sn =∑Xk n = 1, 2, 3, ... . (7-3) 

k =1 

178
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A key characteristic of a Poisson process is that the event interarrival times (IATs) are 

exponentially distributed over the interval (0, t] where IAT = 1/λ and represents the mean time 

between events. 

We analyzed the time variation of the instantaneous values of Ecoh for each 10-minute record for 

which we assumed the process creating Ecoh was at least quasi-stationary and is nominally 

homogeneous Poisson. This means we are assuming that the structures are occurring on a 

continuous basis at a constant rate for the boundary conditions prevalent during the 10-minute 

record. We further assume that two events cannot occur within one sample period (i.e., 0.02 

seconds for Rows 1 and 41 and 0.06 seconds for Row 37 in the California wind farm; 0.025 

seconds for the LIST Project; and 0.05 seconds for the LLLJP). 

The original Ecoh time series was initially smoothed over a 3-second period using a centered 

(non-causal) finite impulse response (FIR) digital filter whose odd numbers of weights were 

based on the specific sampling rate. A detection threshold was used to identify individual 

coherent structures. Because we were interested only in values of Ecoh that could induce at least 

the threshold dynamic response in a turbine, we initially used 2 m

2 

s

–2. We found, however, that 

the turbulence was severe enough in the California wind farm and at Row 4 of the NWTC that 

we detected hundreds of very short coherent structures. We then revised this threshold upward to 

5 m2 s

–2 for these two locations, but found it was adequate for the Lamar site because it was less 

energetic than the others. 

As each individual coherent structure with a 10-minute record was detected, the length and 

intensity or peak values of the smoothed Ecoh were logged. The total length and number of 

coherent structures and the overall peak value of Ecoh found within the record were added to the 

log. These data were annotated with RiTL and the local values of the mean U-velocity 

component, the shearing stress or friction velocity u*, and the vertical velocity standard deviation 

σw to facilitate later scaling in TurbSim. A second data file was created that contained Xn or IAT 

between each of the structures detected. A program was written to process this second data file, 

to first make sure that there were at least 60 seconds between each event and to obtain the mean 

IAT, i.e., the mean time between encountering coherent structures. 

7.7 Measured Turbine Dynamic Response to Observed Coherent Structures

We used the California wind farm Micon 65/13 data set to examine the turbine response to the 

coherent turbulent structures measured by the previous procedure. We were able to obtain 

coherent structures from all but 2 of the 397 records in which we had both the turbulent inflow 

and the matched responses from the two turbines. The information contained within the coherent 

structure data format included inflow parameters that we have shown to scale turbine dynamic 

responses, including the hub U , local u* , RiTL, and σw. We correlated the turbine response 

variable FBM DELs and peak values with the total length of coherent structures in the record, 

Tcoh; the number of these structures, Ncoh; and the maximum value of Ecoh or intensity within the 

record. 

Figure 7-18 presents the correlations of the FBM DELs and peak values with RiTL from the 

matched records. We also annotated these graphs with the CRR stability range (pair of vertical 

dashed lines indicating the range of +0.01 < RiTL < +0.05), the RiTL value of maximum response 

RiTL = +0.02 as a vertical dot-dot-dashed line, and a dotted line (RiTL = +0.10) indicating the 

179
 
 

 

 

 

 

 

 

 

 

 

upper limit of the CRRH stability class. The moderately stable STC04 class extends from the 

dotted line to the right edge of the graph. As we have seen before, the greatest response occurs in 

the CRR range for the reasons discussed previously. 

In Figures 7-19, 7-20, and 7-21 we plot the observed variations of the two Micon 65/13 turbine 

root FBM DELs and peak values with Tcoh, Ncoh, and peak Ecoh of the coherent structures found 

in a population of 10-minute matched records where the peak values of Ecoh > 5 m

2 

s

–2. We 

noticed that the slope of the LOESS-smoothed trend lines with each variation changed 

significantly at some point as the independent variable increased. This suggested perhaps a 

systematic change occurring in the loading process associated with the higher values of these 

coherent structure characteristics. We created a subset of the records in which the FBM DELs 

from the NREL rotor exceeded the P90 (18.95 kNm) of the entire population. Table 7-6 

summarizes the means, medians, and standard deviations of the turbine FBM DELs, the inflow 

turbulence scaling parameters, and the coherent structure attributes for the matched records in 

this subpopulation. This table reveals that the turbine loads in the tail above P90 occur fully 

within the CRR stability class, whose means and medians agree with the value of RiTL = +0.02 as 

stability where we previously found the maximum loads. Also, the distribution central values of 

the hub wind speeds are just slightly above rated (at least for the NREL rotor), and the one 

standard deviation variation about these speeds would coincide with significant unsteady 

aerodynamics of these stall-controlled rotors. Finally, the values of both local u* and σw are high. 

The high value of the shearing stress u* ensures a large reservoir of energy is available to be 

turned into coherent turbulent energy by the action of buoyancy-damped K-H billows, which is 

supported by the high value of σw and the magnitude of the central measures of the mean peak 

Ecoh. 

180
 
Figure 7-18. Correlation of Micon 65/13 FBM DELs and peak values with RiTL from records in which 

peak Ecoh exceeded 5 m2

 s–2. The pair of vertical dashed lines represents the range of the CRR 

stability class, the dot-dot-dashed line the RiTL value (+0.02) of maximum response, and the dotted 

line the upper limit of the CRRH stability class (+0.05 ≤RiTL < +0.10). The moderately stable STC04 

class extends from this dotted line to the limit of the diagram (RiTL = +0.25). 

181 
 

 

 

Table 7-6. Statistics of Matched Micon 65/13 Turbine Responses, Turbulence Scaling Parameters, and
 

Corresponding Coherent Structure Attributes for Peak Ecoh > 5 m2 s

–2 and NREL Rotor FBM DEL > P90 

(18.95 kNm) 

Statistic 

NREL 

FBM 

DEL 

(kNm) 

AeroStar 

FBM 

DEL 

(kNm) 

RiTL 

Hub U 

(m s–1) 

Hub u* 

(m s–1) 

Hub σw 

(m s

–1) 

Coherent Structures 

Tcoh 

(s) 

Peak 

Ecoh 

(m2 s–2) 

Ncoh 

Mean 19.77 18.50 0.020 12.90 1.360 2.323 58.46 18.28 43 

Median 19.60 17.88 0.016 12.93 1.356 2.257 55.43 16.80 42 

Standard 

Deviation 0.784 1.501 0.015 0.813 0.151 0.203 13.11 4.46 9 

182
 
 

Figure 7-19. Observed variations of Micon 65/13 FBM DELs and peak values with total length of 

coherent structures (Tcoh) in a 10-minute record. The vertical dot-dashed line indicates the median 

Tcoh value associated with records with the NREL rotor FBM DEL > P90. The red solid and dashed 

trend lines represent LOESS smoothing with a 0.5 overlap. 

183 
Figure 7-20. Observed variations of the Micon 65/13 FBM DELs and peak values with number of 

coherent structures (Ncoh) in a 10-minute record. The vertical dot-dashed line indicates the median 

Ncoh value associated with records with the NREL rotor FBM DEL > P90. 

184 
 

Figure 7-21. Observed variations of Micon 65/13 FBM DELs and peak values with intensity (peak 

Ecoh) found in coherent structures within a 10-minute record. The vertical dot-dashed line 

indicates the median peak Ecoh associated with records with the NREL rotor FBM DEL > P90. 

185 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

We annotated Figures 7-19, 7-20, and 7-21 with vertical dot-dashed lines corresponding to the 

medians of Tcoh, Ncoh, and peak Ecoh listed in Table 7-6. In all cases the change in the observed 

trends in the slopes of these variables with the turbine responses occurs near the medians 

associated with the largest 10% turbine fatigue loads. This indicates that the turbine responses in 

the high loading tail become less sensitive to one or more of the dynamic characteristics of the 

coherent structures the turbine blades are encountering. To understand what such characteristics 

may be, we plotted the variation of the buoyancy length scale normalized by the NREL rotor 

diameter (Lb /D) as a function of RiTL in Figure 7-22, in which a decaying exponential curve has 

been fitted. We annotated this chart with the P25-P50-P75 of the measured RiTL values 

associated with the FBM high loading tail summarized in Table 7-6. The fitted curve and the 

median of the RiTL values in the high loading tail intersect at a value of Lb /D of one; i.e., the 

buoyancy length scale is equivalent to the rotor diameter. We know from our previous discussion 

in Section 6.2.2 that the buoyancy length scale is the spatial equivalent of the fastest-growing KH instability mode and the source of the greatest dynamic response in the turbine, as depicted in 

Figure 6-7. Going further, in Figure 7-23 we plotted the variation of the measured coherent 

structure intensities (maximum value of Ecoh in a 10-minute record) with Lb/D. We added a 

LOESS-smoothed trend line in red and the median value of the peak Ecoh associated with the 

high loading tail in Table 7-6 as a horizontal dot-dot-dashed line. This line intersects with the 

smooth trend line within the indicated circle at an Lb /D value of 1, which also is the fastest 

growing K-H mode with dimensions of the rotor diameter. So the source of the inflection points 

in Figure 7-21 reflects the change from coherent structures associated with Lb /D from less than 

to greater than one, i.e., the fundamental or fastest-growing K-H modes with scales smaller than 

the rotor diameter to larger with the perfect coupling at Lb /D = 1. 

Table 7-7 summarizes the turbulence and coherent structure parameters taken from the San 

Gorgonio/Micon data set for an Lb/D range of 0.95 to 1.05. This table shows for such conditions 

the mean wind speed into the turbine would be near rated for the NREL turbine and below rated 

for the AeroStar. Although there would be near-perfect to perfect coupling with K-H billows for 

the NREL rotor, it would not be optimum for the AeroStar rotor, which is in part why Table 7-6 

shows the lower loads for it. 

186
 
 

Figure 7-22. Variation of Lb/D ratio for Micon 65/13 (NREL rotor) with RiTL. The black vertical lines 

indicate the P25-P50-P75 range of the RiTL associated with the high loading tail (FBM DEL > P90). 

The stability classes and the max response RiTL = +0.02 are also as red vertical lines. Note that at 

the median RiTL value of +0.016 in Table 7-6, the Lb /D ratio for the NREL rotor is 1 or the buoyancy 

length scale is equivalent to the rotor diameter. This indicates that the fastest growing K-H mode 

is the same scale as the rotor diameter and a source of the high fatigue loads. 

187 
 

 

 

Table 7-7. Inflow Turbulence Parameters and Coherent Structure Characteristics from San Gorgonio Row 

37 Data Set for 0.95 < Lb/Dnrel < 1.05 

Statistic RiTL 

Hub U 

(m s–1) 

Hub u* 

(m s–1) 

Hub σw 

(m s–1) Lb/Dnrel Lb/Daero 

Tcoh 

(s) 

Peak 

Ecoh 

(m2 s

–2) 

Ncoh 

Mean 0.018 11.91 1.272 2.270 1.000 1.063 51.78 17.02 37 

P25 0.016 10.92 1.118 2.172 0.980 1.041 43.56 14.71 33 

Median 0.016 12.16 1.302 2.220 1.002 1.065 49.24 16.05 39 

P75 0.020 12.79 1.419 2.364 1.020 1.084 61.29 18.44 41 

Standard 

Deviation 0.006 1.117 0.234 0.183 0.028 0.030 12.56 3.52 7 

188
 
 

 

 

 

 

 

 

Figure 7-23. Observed variation of intensity of the coherent structures (peak Ecoh) within a 10­

minute record as a function of buoyancy length scale Lb normalized by Micon 65/13 NREL rotor 

diameter. The median of the peak Ecoh (16.80 m2 s–2) in Table 7-6 for the high loading tail shown by 

the dot-dot-dashed horizontal line. This value intersects with the LOESS-smoothed trend line at a 

Lb /D ratio of 1 as highlighted by the circle. 

7.8 Observed Coherent Structure Characteristics 

Figure 7-24 plots the measured probability distributions of peak Ecoh, Tcoh, and Ncoh for the three 

locations within the California wind farm (upwind of Row 1, upwind of Row 37, and downwind 

of Row 41), upwind of the NWTC ART, and on the LLLJP 120-m met tower. In Figure 7-25 we 

plotted the corresponding probability distributions of the local mean U-velocity component, the 

shear stress or u*, and the standard deviation of the vertical velocity component σw. As would be 

expected, the characteristics of the coherent structures upwind and within the wind farm vary 

with the location, as do the three turbulence parameters, U , u*, and σ w. The most energetic 

structures occur at the NWTC and the least energetic at the Lamar site. Figure 7-25 shows that 

the wind farm is distinguished by the significant spatial heterogeneity, which influences the 

characteristics of the coherent turbulent structures. Compared with the Lamar site, the vertical 

heterogeneity of the NWTC (seen particularly in the local friction velocities [u*] and the vertical 

wind field [σw]) is responsible for the energetic characteristics of the coherent structures. Figure 

7-26 shows that for the NWTC site, the greater the length of coherent structures within a 10­

minute record, the greater the intensity. 

189
 
Figure 7-24. California wind farm, NWTC, and Lamar probability distributions of measured coherent structure ch

minute records: intensity (peak 

Ecoh), total length (

Tcoh), and number of structures (

Ncoh) 

190 
Figure 7-25. California wind farm, NWTC, and Lamar probability distributions of local U, friction velocity u*, an

standard deviation σw corresponding to measured coherent structure characteristics in Figure 7

191 
Figure 7-26. NWTC measured variation of peak Ecoh with Tcoh within a 10-minute record 

To apply the distributions of coherent structures in TurbSim, we need to scale the rate parameter 

 (or equivalently IAT = 1/) in Equation 7-2 to accommodate the inhomogeneous Poisson 

distribution model. Our analysis has shown that  = f[U(z), RiTL] are the dominant scaling 

parameters. In Figure 7-27 we summarize the variations of IAT as a function of the local mean U 

velocity and RiTL for the three locations in the wind farm, the NWTC, and the Lamar site. For the 

wind farm, both velocity and stability vary greatly. Comparing the San Gorgonio upwind 

location with the NWTC and Lamar sites, we see that the variations with both velocity and 

stability are similar because they were measured in naturally occurring flows. Although the 

NWTC has a large degree of variation , probably because of the high level of flow heterogeneity 

within the ART rotor disk, the distributions with stability are similar for all three sites, i.e., much 

shorter IAT in and near the CRR stability range compared with longer periods outside of it. The 

natural flows have distinct variations in IAT with velocity. At lower wind speeds the periods are 

192 
 

 

 

 

 

 

 

longer and there is more variation, but there is a point at all three sites where the IAT suddenly 

becomes much shorter and has less variation. The IATs for the NWTC and Lamar site 

asymptotically approach the same value of 70 seconds for wind speeds greater than 20 m s–1 and 

more than four times shorter than the IATs seen at 5 m s

–1 . 

As turbine rotors increase in diameter and their hub heights ascend deeper into the atmospheric 

boundary layer, it is important to determine the coherent structure scaling parameters with these 

increased elevations. To date, our measurements from these greater heights come from the 

LLLJP and its 120-m tower. We plotted contours of the IAT and Ncoh as functions of the local 

velocity U and turbine layer stability RiTL for 54, 67, 85, and 116 m in Figure 7-28. To see how 

the maximum Tcoh varies with height, we summarize the data from all three sites in Figure 7-29. 

Although lengths of coherent structures are relatively short at the wind farm, the variations with 

height in the natural flows from the NWTC and the Lamar site are very consistent. 

193
 
 

 

Figure 7-27. Variations of coherent structures IAT with local U velocity and RiTL for upwind of Rows 1 and 37 and downwind of Row 41 

in California wind farm; at 15-, 37-, and 58-m heights at NWTC; and at 54-, 67-, 85-, and 116-m heights at LLLJP site. The vertical dashed 

lines in the upper row represent the nominal rated wind speeds and those in the lower row represent the stability classifications. 

194 
Figure 7-28. Variations of IAT and Ncoh with height and local U velocity and RiTL at LLLJP site. The 

horizontal red line represents a nominal turbine rated wind speed of 12.5 m s–1 and the vertical 

black lines represent the stability classifications. 

195 
 

Figure 7-29. Observed variation of maximum Tcoh as function of height for California wind farm,
 

NWTC, and LLLJP sites
 

196
 
 

 

 

 

 

 

 

 

 

 

8.0 Supporting the Extension of Larger Turbine Rotors to Higher 

Elevations in the Great Plains Operating Environment 

As we’ve noted, the trend has been toward larger turbine rotors with the higher hub heights to 

take advantage of better wind resources. This is particularly true over much of the Great Plains, 

which contains the greatest resource in the United States. The northern plains benefit from the 

winter storm tracks that bring strong winds to these regions. In the southern plains, however, the 

best wind resources occur in the warmer months from April through September, but generally at 

night. This nighttime low-level jet (LLJ) of air occurs from West Texas northeastward into 

northwest Iowa and southwest Minnesota. This excellent nocturnal wind resource arises from 

diurnal atmospheric boundary layer dynamics that create a low-level, higher speed region of 

wind flows between 70 and about 500 m above the ground. 

Because of the fundamental thermodynamic diurnal cycle in the atmospheric boundary layer, 

such nocturnal wind systems are far more prevalent beyond the Great Plains, though they often 

are more localized, such as in and around terrain features with at least moderate changes in 

elevation. In addition, such nocturnal flows have lower frequencies of occurrence and strengths. 

They do all have in common, however, often intense vertical wind speed and sometimes 

directional shears within the height elevations or layer of multimegawatt wind turbine rotors. 

Increasingly warmer temperatures usually accompany this increase in wind speed with height , 

creating a statically stable environment below the height of the wind speed maximum. When 

these vertical temperature and wind speed gradients are combined, they define the degree of 

dynamic instability that exists, which can be quantified by the gradient Richardson number (Ri). 

As we have seen, the relative strengths of the negative buoyancy associated with a stable 

environment and the turbulent energy contained within the sheared wind flow determine if 

turbulence will be generated and, if so, its intensity and spatial characteristics. We showed that 

given the right vertical variations in temperature and wind speed, Kelvin-Helmholtz Instability 

(KHI) can develop and create organized or coherent turbulent patches that induce undesirable 

dynamic responses in wind turbine structures. 

Although no concurrent turbine measurements were available during the Lamar LLJ Project 

(LLLJP), we now can interpret these results based on we learned from the field campaigns in the 

San Gorgonio wind farm and its Micon 65/13 turbines and the Advanced Research Turbine 

(ART) at the National Wind Technology Center (NWTC). These discussions will be useful to the 

wind turbine community because they represent the interpretation of atmospheric conditions seen 

by the current deployment of large, multimegawatt turbines at heights much higher than 

previously had been available. As we discuss later, we attempted to create a comprehensive 

simulation of this inflow conditions with the Great Plains Low Level Jet, or GP_LLJ, spectral 

model in the TurbSim stochastic simulator code. 

8.1 Interpreting LLLJP Results 

In our previous discussions we have shown that the dynamic response seen in wind turbine 

structures to the turbulent inflow results from the ingestion of organized or coherent patches of 

turbulence into the turbine rotors. We have shown that these patches of turbulence arrive in a 

rotor inflow after evolving directly upstream as well as being created at heights outside of the 

rotor layer and then carried into it by vertical motions. 

197
 
 

 

 

 

 

 

 

 

 

 

 

 

8.1.1 Analyzing the Lamar Measurement Database

We analyzed the year record from the 120-m LLLJP met tower for 1600 to 0800 LST in terms of 

the key turbulence scaling parameters that we identified using the Micon turbine and ART inflow 

measurements and dynamic responses. These include the hub-height mean wind speed, the mean 

shear, and shearing stress (u*) across the vertical dimensions of a GE 1.5-MW turbine rotor disk 

stratified by stability classification. After removing records that did not pass our stringent quality 

control criteria and where the flow was coming through the tower, we were initially left with 

28,594 ten-minute records. This figure represents 82% of the records that would be expected if 

no data were lost and if quality control and flow distortion considerations were ignored. To make 

the statistical analyses more meaningful, we retained only records in this reduced data set in 

which a turbine would be operating, which is a hub-height (85-m) mean wind speed between an 

approximate cut-in of 3.5 m s–1 and cutout of 25 m s–1. This further reduced the final data volume 

available for analysis to 27,544 records, or 79% of those expected. In Table 8-1 we summarize 

the distribution of this final data volume by stability class. One would expect the important CRR 

stability class to occur about 5% of the time at this site. We did not analyze the records when 

RiTL ≥ +1.0 because the data became highly suspect owing to very unsteady flow conditions that 

created observational issues of one sort or another. We also chose to ignore the most unstable 

classification STC01 because so few records were available. 

Table 8-1. Distributions of LLLJP Nocturnal Data Records by Stability Class after Applying Described 

Constraints
 

Stability Class Stability Range Records Hours Percent 

STC01 -1 ≤ RiTL 299 50 1.2 

STC02 -1 < RiTL ≤ 0 2040 340 8.4 

CRR +0.01 ≤ RiTL < +0.05 1225 204 5.0 

CRRH +0.05 ≤ RiTL < +0.10 2888 481 11.8 

STC04 +0.10 ≤ RiTL < +0.25 6359 1060 26.1 

STC05 +0.25 ≤ RiTL < +1.0 7504 1251 30.8 

RiTL ≥ +1.0 3944 657 16.2 

We saw in our analysis of the Micon 65/13 turbines and the ART that their dynamic response is 

strongly correlated with peak Ecoh because of the coherent characteristics of KHI turbulence. 

Figure 8-1 plots the diurnal distribution of peak Ecoh measured by the four sonic anemometers at 

54, 67, 85, and 116 m on the LLLJP 120-m tower. Here the lower abscissa is calibrated in UTC 

time and the upper one is in equivalent local standard time (LST). The dynamic response 

thresholds found on the Micon turbines and the ART are indicated as a horizontal dot-dot-dashed 

line for the threshold response of 2 m2 

s

–2, a dashed line for the moderate response level 5 m2 

s

–2 , 

and a solid line for significant response level of 10 m2 

s

–2. The highest levels of coherent TKE 

occur most frequently between local sunset and midnight (1700 to 0000 LST or 2300 to 0900 

UTC), i.e., in the boundary layer day-night transition period. This is in agreement with the 

diurnal variations seen in the wind farm and at the NWTC. Although not as energetic as at the 

internal wind farm and NWTC sites, values of Ecoh exceeding 20 m2 

s

–2 do occur. Figure 8-2 

displays the non-Gaussian cumulative probabilities of the peak Ecoh at the four measurement 

heights. Coherent events with intensities greater than the significant response threshold level of 

10 m2 

s

–2 are more or less equally probable to occur 2% of the time. In contrast, moderate level 

responses or greater would occur 10% or more of the time. 

198
 
 

Figure 8-1. Diurnal distribution of observed 10-minute record peak Ecoh values measured at 54-, 67, 

85-, and 116-m heights on LLLJP 120-m turbine at 1700–0800 LST (0000–1500 UTC). The three 

turbine response thresholds measured on the Micon 65/13 turbines and the ART are shown as the 

dashed and solid horizontal lines. 

199 
 

Figure 8-2. Observed LLLJP probability distributions of peak Ecoh over 54- to 116-m layer. The dotdashed, dashed, and solid vertical lines indicate the threshold (2 m2 s–2), moderate (5 m2 s–2), and 

significant (10 m2 s–2) dynamic response levels seen on the turbines. 

200 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Because the stability of the turbine layer is a major factor in the scaling of the turbulence and the 

subsequent turbine dynamic response, with the critical Richardson number range, or CRR, being 

the most important, we examine the cumulative probability distribution of RiTL in Figure 8-3. 

Here the CRR stability range is indicated by the pair of vertical dashed lines. The inset on the 

upper left indicates that CRR conditions existed during 285 hours or 7% of the aggregate filtered 

record length. The combined ranges of the CRR and CRR High, or CRRH, classes form the 

STC03 classification, which we used when we developed the TurbSim Code; it occurs 20% of 

the time. Within the CRR range we see in Figure 8-4 that the most prevalent intensity of coherent 

events is at the moderate turbine dynamic response level. Events with intensities greater than the 

significant response level occur more often, however, than would be expected if the distribution 

were normally distributed. 

We now plot in Figures 8-5 and 8-6 for the stability classifications the cumulative percentile 

distributions of both the key scaling parameters and the associated turbulence characteristics that 

we previously showed are important in determining the level of turbine dynamic response. As we 

saw previously in the wind farm and at the NWTC, the highest hub-height mean wind speeds are 

associated with the CRR class, as shown in Figure 8-5a. This means, of course, with the stronger 

background flow more energy is available to create more intense levels of KHI turbulence and 

greater turbine dynamic responses. The strong vertical mixing associated with such turbulence 

reduces the vertical shear, as is shown by the rotor disk shear exponent distributions in Figure 8­

5b. Only the unstable STC02 class has lower shears; the remaining classes all exhibit significant 

values. This transfer of energy from the background flow into turbulence by the KHI is 

documented by the rotor layer mean shear stress or u* for the CRR range when compared with 

the other stability classes in Figure 8-5c. The frequent high levels of peak Ecoh in Figure 8-5d 

demonstrate why larger turbine loads and fatigue exist in the CRR range. Figure 8-5d also 

reveals that the KHI mechanism can create larger variations in the vertical velocity in this 

stability range than the large convective eddies seen in the STC02 unstable class. We showed 

that the largest and most damaging loads occur in the CRR range when the buoyancy length 

scale normalized by the rotor diameter D is Lb/D ≈ 1; this is demonstrated in Figure 8-5e. Here 

we highlight the P25–P75 (Q1–Q3) range over which the the Lb/D parameters varies from 0.5 to 

a bit more than 1. Even at Lb/D ratios of less than 1, some vibrational energy is likely to be 

transferred from the coherent turbulence into the turbine rotor, nacelle, and tower given the 

blade’s second symmetric and asymmetric modes and numerous modal cross-couplings found in 

the eigenvalue analysis of the 1.5-MW WindPACT turbine listed in Table 7-2. 

Turbulent fluxes or transports may not be uniform across the 1.5-MW turbine rotor disk and 

larger turbines, as is shown in Figures 8-6a and b. Here we see that Lb Q1–Q3 variation over the 

upper half of the turbine rotor is from 0.5 D to about 0.7 D with a median of 0.6 D. In the lower 

half it is from 1.0 D to about 1.15 D with a median of about 1.1 D. As we saw with the Micon 

turbines and the ART, the largest peaks in the mometum (u′w′) and buoyancy (w′T′) fluxes across 

the depth of the rotor are skewed downward, as indicated by the negative tail P01, P05, and P10 

percentiles. 

201
 
Figure 8-3. Observed LLLJP probability distribution of RiTL for filtered data set 

Figure 8-4. Observed LLLJP probability of hub-height peak Ecoh within the CRR range. The 

dynamic response thresholds from the Micon turbines and the ART are shown as vertical dashed 

lines. 

202 
 

(e) (d) 

(c) (d) 

(a) (b) 

Figure 8-5. Observed LLLJP percentile probability distributions key scaling and turbulence 

parameters associated with turbine dynamic response for reduced analysis data set by stability 

class 

203 
(d) 

(c) 

(b) 

(a) 

Figure 8-6. Observed LLLJP percentile probability distributions of variation by stability class of 

buoyancy length scale Lb in (a) upper half rotor disk (85–116 m) and (b) lower half (54–85 m). The 

cross-hatched areas indicate the P25–P75 (Q1–Q3) range. The distributions of the rotor layer peak 

momentum (u′w′) and buoyancy fluxes (w′T′) are shown in (c) and (d), respectively. 

Intense vertical fluxes of Ecoh are concentrated in the CRR range, as shown in Figure 8-7. Figure 

8-8 displays an example of such fluxes beneath an LLJ. Here we present a portion of a fixed 

azimuth, vertical sector scan from the NOAA HRDL lidar taken between 18:11:12 and 18:11:34 

MST (01:11:12 to 01:18:34 UTC) on September 15, 2003. Energetic turbulence is indicated 

within the layer that would be occupied by a GE 1.5-MW turbine rotor, with strong downward 

bursts of higher speed air indicated by the arrows. A series of K-H billows might exist between 

50 and 70 m, with a horizontal wavelength of about 100 m. 

204 
Figure 8-7. Observed peak instantaneous vertical fluxes of Ecoh as function of height across
 

WindPACT rotor disk: (a) downward and (b) upward 

205 
Figure 8-8. Portion of fixed azimuth, vertical sector scan measured by NOAA HRDL lidar on 

September 15, 2003, 18:11:12 to 18:11:34 MST. The vertical arrows indicate strong downward 

bursts of higher velocities into the shear layer below a 20-m s–1 LLJ at about 200 m, which would 

be occupied by a GE 1.5-MW turbine rotor. There is some indication that KHI also may exist. 

206
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

8.2 Role of the Great Plains LLJ in Coherent Turbulence Generation and 

Transport within the Rotor Disk

We noted previously that the stable layer accompanied by intense shear beneath a low-level jet 

maximum velocity is a prime environment for the development of KHI and one of the major 

reasons for undertaking the LLLJP. The information that we gathered from this effort was used 

to develop the TurbSim GP_LLJ spectral model discussed in the next section. 

In addition to collecting measurements from the LLLJP 120-m met tower, we needed to obtain 

vertical LLJ wind speed and direction profiles up to at least 500 m above ground level (AGL). 

As we will see, a jet maximum located well above the top of a wind turbine rotor can still have 

significant influence within the rotor disk and thus we need to examine this maximum height. 

The instrument used to obtain the velocity profiles was a midrange Scintec MFAS sodar 

programmed to measure the speed and direction over 20-m increments from 40 to 500 m. We 

also recorded the standard deviations of the horizontal and vertical wind components, though 

they are not always reliable, particularly the horizontal standard deviation. In Figure 8-9 we 

present an example of raw (circles) and smoothed (red lines) sodar-derived wind speed and 

direction profiles collected on September 9, 2002 at 0730 LST. The raw sodar profiles were 

smoothed with a Chebyshev polynomial recursively up to 10th order. Met tower data were used 

to derive the profiles between the lowest sodar measurement and the lowest tower measurement 

(3 m). The chart on the right in Figure 8-9 indicates a measure of the sodar signal-to-noise ratio 

or confidence level for each measurement height. A value of 1 is the poorest and 4 is the best. 

We used only profiles that had values of 3 (high confidence) or 4 (very high confidence). The 

plot shows an LLJ speed maximum at 241 m AGL (a common LLJ height). 

8.2.1 Case Studies for June 17, 2002 

The role of the jet stream in influencing turbulent conditions within the turbine layer is well 

demonstrated by conditions seen in the early morning and again in the day-night transition period 

of June 17, 2002. Figure 8-10 displays the 10-minute mean wind speed profiles measured by 

sodar for these two periods. Figure 8-10a documents the jet evolution between 0010 and 0400 

LST (0710 to 1100 UTC) in 10-minute increments. Though fluctuating, the jet height is 

nominally about 250 m AGL. In contrast, Figure 8-10b plots the vertical profiles from 1900 to 

2350 LST (0200 to 0650 UTC). In this case the jet maximum is at 200 m AGL. There is a stark 

contrast in the behavior of the jets in these two time periods. The jet during the early morning 

hours is higher and weaker and becomes stable with a maximum velocity of 19 m s–1 and intense 

vertical shear after about 0230 LST. During the day-night transition the next evening, the jet 

begins to form around 1910 LST. It gradually gains both strength and height until reaching a 

maximum speed of 25 m s–1 at 250 m AGL at 2140 LST. At this point it becomes unstable and 

breaks down into strong turbulence, which mixes out the shear significantly. 

207
 
208 

Figure 8-9. Example of raw (circles) and smoothed (red lines) sodar-measured wind speed and 

direction profiles with the tower data used to extend lower limit to 3-m height. The rightmost 

graph plots the measurement confidence level, a measure of the sodar signal-to-noise ratio, with 1 

being the poorest and 4 the best. The lower dot-dashed lines indicate the height range of a GE 1.5-

MW turbine and the upper dot-dot-dashed line is an estimate of the maximum upper height of a 

future 10-MW turbine. The jet maximum was at 241 m AGL.

 

WD 

degs 

225 270 315 360 

z (m) 

0 

100 

200 

300 

400 

500 

UH 

ms-1 

6 8 10 12 14 16 

Sodar Conf Level 

1 2 3 4 

0 

100 

200 

300 

400 

500 

0209130730 

Jet Max Height 241 m 
 

Figure 8-10. Profiles on June 17, 2002, 1900 to 2350 LST. Jet on left (a) remained stable and did 

not break down. Jet on right (b) broke down into turbulence after 2100 LST. The lower dashed 

lines outline the height range of a GE 1.5-W turbine and the upper longer dashed line represents a 

possible maximum height of a 10-MW turbine. 

209 
 

 

 

 

 

 

 

 

 

 

 

 

We now document the turbulent conditions seen in the layer measured by the 120-m met tower, 

which would have been experienced by a GE turbine. Figure 8-11 compares the time series of 

the time variation of both the background flow conditions and the turbulence parameters for the 

early morning period (Figure 8-11a) and the day-night transition (Figure 8-11b). The plots in the 

topmost row (Figures 8-11a and d) display the variations in the hub-height mean U speed and 

RiTL. A well-established LLJ exists at the beginning of the period, and the wind strength and 

stability support the generation of fairly intense coherent turbulence (Figure 8-11b) with a 

dominant buoyancy length scale Lb /D of 0.5 to 0.6 (Figure 8-11c). As time goes along, however, 

the turbine layer stability increases and the damping slows the winds and reduces the coherent 

turbulence level, which also significantly shortens the buoyancy length scale and the coupling to 

a turbine rotor. 

The day-night transition characteristics in the right column of Figure 8-11 in some ways mirror 

those of the early morning event sequence. Initially the stability suppresses both the jet formation 

and turbulence in the turbine layer, but at about 2040 LST destabilization begins and the jet 

velocity increases. As the jet peak velocity continues to increase, a relatively rapid 

destabilization and turbulent breakdown occurs between 2050 and 2100 LST, creating strong 

vertical motions (Figure 8-11e) and coherent turbulence with buoyancy length scales closely 

equivalent to the rotor diameter (Figure 8-11f). Just before 2200 the turbine layer goes fully 

turbulent as RiTL approaches +0.02, the coherent turbulence level exceeds the significant 

response threshold of 10 m2 s

–2, and the buoyancy length scale becomes greater than the rotor 

disk diameter. This intensification of the LLJ was responsible for creating significant coherent 

turbulence activity within the rotor disk and increased loads and fatigue on turbine components. 

These two case studies are an excellent example of how the turbine layer dynamic stability plays 

a crucial role in the generation of coherent turbulence at the scales of turbine rotor. In Figure 8­

12 we plot the disk-normalized buoyancy length scale Lb/D as a function of the RiTL with the 

CRR, CRRH, and STC04 stability class boundaries annotated for these two June 17 

observational periods. It is clear why we have referred to the CRR range as “critical,” with the 

CRRH range as a transition to the highly damped turbulent environment of STC04. 

210
 
Figure 8-11. Turbulent and background flow characteristics for June 17, 2002, morning and 

evening case studies. The hub-height (85-m) mean wind speed U and RiTL are plotted in (a) and 

(d); the hub-height σw and peak Ecoh are plotted in (b) and (e); and the disk-diameter normalized 

buoyancy length scale Lb /D and the turbine layer buoyancy frequency Nbuoy in (c) and (f). 

211 
Figure 8-12. Observed variations of buoyancy length scale of mean rotor disk layer with RiTL for 

0010 to 0400 LST and 1900 to 0000 LST on June 17, 2002 

212
 
 

 

 

 

 

 

 

 

 

 

 

 

 

8.2.2 Lidar Measurements of LLJ-Induced Turbine Layer Coherent Turbulence

We were fortunate to have had the NOAA HRDL lidar to help us visualize and confirm the role 

of the LLJs in influencing the coherent turbulence seen within turbine rotor layers beneath the 

LLJs. In the early morning hours of September 9, 2003, we observed coherent waves present 

beneath an LLJ whose peak velocity was about at about 230 m AGL at the Lamar site. As part of 

our procedure, we aligned the HDRL laser beam into a fixed azimuth aligned with the mean 

wind direction (as determined by the sodar) and a 10 degree fixed elevation angle. This allows us 

to measure the wind velocity as it passes through each of the hundred 30-m wide velocity range 

gates with a vertical resolution of 5 m at a sampling rate of 4/s. Using various signal processing 

techniques when postprocessing these data, we were able to produce the contour plots of Figure 

8-13. Banta and coauthors (1997) showed that in stable flows, TKE (or ET) can be estimated 

from the HRDL velocity measurements. 

In Figure 8-13a we plotted contours of the estimated TKE, whose intensity is color coded by the 

legend in the upper left of the diagram. The corresponding instantaneous TKE values directly 

measured by the sonic anemometers on the met tower are shown in the lower panel. In Figure 8­

13b we added the lidar-derived mean vertical wind profile for the period of the observation, 

shown as a white dot-dot-dashed line annotated as Ulidar(z). We superimposed the corresponding 

profiles of the horizontal wind speed [solid white line, Usodar (z)] and the vertical velocity 

standard deviation (yellow line, σw) as measured by the sodar. These profiles indicate that the 

vertical turbulent fluxes or transports may not be uniform across the rotor disk. In the lower 

panel of Figure 8-13b we plotted the instantaneous values of Ecoh measured by the sonic 

anemometers with the minimum and moderate dynamic response thresholds indicated by dashed 

lines. The lower extent, hub, and upper extent of a GE 1.5-MW turbine are shown as horizontal 

light dashed lines on both of the contour plots. 

Figure 8-13b visibly demonstrates the relationship between the shear intensity and the 

development of patches of coherent turbulence. It also shows moderate vertical motions just 

above hub height. The tower measurements of Ecoh in the lower panel confirm that many of the 

structures seen in the contour plot have coherent energy intensities greater than the minimum 

response threshold, with the most intense at about 450 seconds. In Figure 8-14 we plot the time 

series of the instantaneous Reynolds stress components ( u w' ', ' ' u w, and vw ' ' ) and their vector 

sum Ecoh measured by the sonic anemometers. We highlighted several of the more intense 

structures (a–f) and the period (f) when the structures are vertically correlated. We plotted the 

instantaneous values of Ecoh and the associated instantaneous buoyancy fluxes ( wT ' ' ) over the 

same time period and marked the same structures seen in Figures 8-15a–f and the vertically 

correlated region (g). A close examination of these structures reveals that the coherent turbulent 

bursts are always associated with negative buoyant fluxes, which add damping to the largest 

turbulent eddy structures. 

213
 
Figure 8-13. NOAA HRDL lidar observations of coherent turbulent patches: (a) lidar estimated TKE 

patches in upper panel with corresponding tower measurements below; (b) same as (a) but with 

mean wind speed U(z) profile (dot-dot-dashed line) with corresponding sodar-measured wind 

speed and σw profiles (yellow line). Time series of the instantaneous measurements of Ecoh at the 

four heights on the met tower are shown in the lower graph. The light dashed lines outline the 

bottom, hub, and top of the WindPACT (GE) 1.5-MW turbine rotor. The minimum threshold and the 

moderate dynamic response levels are shown in the lower graph of (b) as horizontal dashed lines. 

214 
 

Figure 8-14. Time series of tower-measured instantaneous Reynolds stress components and Ecoh 

values corresponding to HRDL profiles in Figure 8-13 between 330 and 480 seconds. Individual 

coherent structures are indicated by dashed lines marked (a–f) and vertically correlated structures 

are indicated by the rectangle identified as (g). 

215 
Figure 8-15. Time series plots of instantaneous local values of buoyancy flux wT ' ' and Ecoh for 

330 and 480 seconds in Figures 8-13 and 8-14. The same coherent structures identified in Figure 

8-14 are marked with the same letters. The effects of turbulent damping can be seen on each of 

the identified individual structures. 

216 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

8.2.3 Low-Level Jet Statistical Characteristics 

To simulate LLJs in the TurbSim Code, we needed to know more about their statistical 

properties which then could be introduced as part of the intended stochastic variation in the 

simulations. We derived the bulk of this information from the sodar observations at the Lamar 

site taken between May and November 2002. After applying postprocessing and quality control 

procedures, we had more than 9,000 ten-minute vertical profiles of mean wind speed and 

direction that contained at least one LLJ between 70 and 500 m AGL. LLJs not only have a 

distinct vertical wind speed profiles, i.e., one or more inflexion points, but also have 

characteristic wind direction profiles. With turbine rotor sizes increasing, we needed to include 

the direction profiles as well to estimate the effects of vertical directional shear in TurbSim Great 

Plains model simulations. 

In Figure 8-16 we present histograms of the lowest jet maximum velocities and the 

corresponding wind directions derived from the 4,466 profiles whose usable maximum 

measurement height reached 500 m. We annotated the maximum velocity plot (Figure 8-16a) 

with the maximum rotor elevations of the GE 1.5SE, the National Renewable Energy Laboratory 

(NREL) 5-MW Reference Turbine, and a future land-based 10-MW turbine. Although not 

applicable directly to the sodar measurements, we annotated the direction histogram in Figure 8­

16b to indicate the direction exclusion range for which the flow passes through the tower 

structure. This exclusion is important when the tower measurements are correlated with the sodar 

profiles. Corresponding to Figure 8-16, we plot the boxplot probability distributions of the 

lowest jet wind speeds with height in Figure 8-17. Figure 8-18 plots the vertical variation of the 

same information as contours varying with time for 1600 and 0800 LST (2300 to 1500 UTC). 

This plot shows that the strongest and highest jets occur between about midnight and 0300 LST 

but are strongest nearest the ground between 1900 and 2300 LST (0200-0600 UTC) during the 

late day-night boundary layer transition period. Figure 8-19 summarizes the variation of vertical 

wind direction shear beneath the measured jets. Here we plot probability (Figure 8-19a) and 

cumulative probability plots (Figure 8-19b) of the distributions of mean and maximum wind 

direction shear between 50 m AGL and the height of the lowest jet. Generally these tend to be 

small, but long tails do exist. 

217
 
Figure 8-16. Observed frequency distributions of (a) lowest jet heights and (b) corresponding wind 

direction for May–November 2002 at Lamar site 

218 
Figure 8-17. Probability variations of maximum velocities of lowest jets with height 

219 
Figure 8-18. Observed variation of wind speed of lowest LLJ height for Lamar site for May–
 

November 2002
 

220 
Figure 8-19. Probability distributions of variations of wind direction shear from 50 m to height of 

the lowest jet: (a) probability and (b) cumulative probability 

221 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8.2.4 LLJs and Turbulent Coherent Structures 

Nocturnal LLJs in the Great Plains in particular are more frequent and intense during what has 

been described as the warm season—April through September (Panofsky and Dutton 1984; 

Mitchell, Arrit, and Labas 1995; Whiteman, Bian, and Zhong 1997). This was a consideration in 

choosing the first 2 weeks of September for the observation period with the NOAA HRDL lidar: 

we wanted to document the seasonal shift from “warm” to “cold” periods, which takes place 

during September. Several theories exist about why the preference for southerly winds occurs. 

Great Plains nocturnal LLJs are much more likely to form when boundary layer winds through 

the region have a strong southerly component, and this occurs more often in the warmer months 

(Panofsky and Dutton 1984; Whiteman, Bian, and Zhong 1997). We found this was certainly 

true from May through November 2002 at the Lamar site, where the median wind direction for 

the jets measured was 199 degrees as shown in the histogram of Figure 8-16b. 

Given this warm season, we wanted to see its effect if any on producing conditions that increase 

dynamic loading of turbines, such as the presence of coherent turbulent structures. First we 

divided the available data record into two subsets, one of which had at least one coherent 

structure within the rotor disk layer and one in which there were none. In Figure 8-20a we 

present a histogram of the percent occurrence of the STC02, STC03, STC04, and STC05 

stability classes in which coherent structures did or did not occur. Here we more finely divided 

the STC02 class into two sub-ranges one of which is narrow and weakly unstable while the other 

is wider and more unstable. We combined the CRR and CRRH classes into STC03 for use with 

the later scaling of TurbSim. We can see that coherent turbulent structures are most frequent in 

the weakly stable STC03 stability class, as might be expected based on our previous discussions. 

In Figure 8-20b, we again differentiate between the presence and lack of coherent structures 

within the rotor disk layer. With the exception of the most stable class, the mean hub wind 

speeds equal or exceed the corresponding rated values. 

To understand the worst case situations for simulation purposes, we correlated stability and hub 

mean wind speed conditions when coherent turbulent structures were found simultaneously at all 

four tower measurement heights within the nocturnal turbine layer at the Lamar site. Figure 8-21 

summarizes our results. We plotted two slightly different presentations of the interquartile range 

(IQR; P25–P75 or Q1–Q3) distributions of RiTL. In Figure 8-21a, the monthly IQR distributions 

as a function of RiTL with the warm season months are shown in red. In Figure 8-21b, the RiTL 

IQR is plotted for each month of the year. We annotated each figure with the stability classes 

CRR, CRRH, STC04, and STC05 and note that the class STC03 is composed of CRR and 

CRRH. We present the IQR distributions for the hub-height mean wind speed in the same 

formats in Figures 8-21c and d. We annotated this figure with the rated wind speeds for the 

WindPACT and NREL 5-MW Reference virtual turbines. We find that the highest observed 

nocturnal wind speeds are prevalent from April through June, with June having the best winds. 

Based on an earlier 2-year wind prospecting record from this site, we believe that the dip in the 

wind speeds in July is an anomaly for this particular year because of intense drought conditions 

(intense subsidence that created very high surface air temperatures) that summer, which peaked 

in July. The July distributions are probably closer to those seen in May in more normal years. 

From Figure 8-21b, when coherent structures are simultaneously occurring at all levels of the 

120-m tower in April, May, and June, we see that CRR stability conditions are also taking place 

at least 50% of time and are accompanied by above-rated wind speeds. At this site then, these 

222
 
 

 

 

three months, and possibly July as well in a more normal year, are productive from a power 

generation perspective, and it is very likely that the level of cumulative fatigue damage in turbine 

components is also high. August and September are less energetic, but they still may be 

contributing a significant amount of damage. It is very likely that LLJs are the dominant source 

of the conditions that are responsible for what we are seeing in Figure 8-21. So it is critical that 

TurbSim be capable of simulating the details of the flow conditions indicated. 

223
 
 

 

Figure 8-20. Available distributions of (a) stability classes; and (b) hub-height mean wind speeds 

by stability class with coherent structure (w/CS) and without (wo/CS) within the rotor layer. Rated 

wind speeds for the WindPACT and NREL 5-MW Reference turbines are indicated by blue dashed 

and dot-dot-dashed lines, respectively. 

224 
Figure 8-21. Monthly IQR distributions of (a) and (b) RiTL; and (c) and (d) hub-height mean wind speed U. The low-

is highlighted in red. The stable stability classes are annotated in red in (b) and the rated wind speeds for the Win

MW Reference turbines are shown as dashed lines in blue in (c) and (d). 

225 
 

 

 

 

 

 

 

 

 

 

 

 

9.0 TurbSim Scaling—A Brief Overview 

9.1 Background 

The TurbSim stochastic inflow turbulence code generates numerical simulations of full-field 

flows that mimic the statistical characteristics of atmospheric boundary turbulence present in 

both natural and internal wind farm environments over a wide range of operating conditions. 

These simulated wind fields are then used to create the wind and turbulence input to aeroelastic 

design codes used to model the dynamic response of actual wind turbine structures. TurbSim was 

specifically designed to interface with the National Renewable Energy Laboratory (NREL) 

AeroDyn aerodynamics routine (Moriarty and Hansen 2005) used with the NREL FAST design 

code (Jonkman and Buhl 2005) and the commercial MSC.ADAMS multi-body dynamics 

simulation code. 

TurbSim has its origins in the seminal work of Paul Veers in his SNLWIND stochastic inflow 

simulator (Veers 1988) and more recently Kelley’s expansion of Veer’s work into the diabatic 

(non-neutral) full-field, full vector flow simulator SNLWIND-3D (Kelley 1992). Most designers 

depend on inflow simulations that are based on one of the normal turbulence models (NTMs) 

recommended by International Electrotechnical Commission (IEC) in their 614001-1 standard 

(IEC 2005). The latest revision includes an implementation of the Mann uniform shear 

turbulence model (Mann 1998) and recommends its use, although a neutral version of the Kaimal 

et al. (1972) spectral model is still included and accepted. While the Mann model is very 

sophisticated (it applies turbulence rapid distortion theory to a sheared flow) and includes 

explicit physics, it still assumes neutral stability as does the much more empirical Kaimal model. 

The Mann model is less encumbered in this regard, but the Kaimal model is based on neutral 

surface layer (SL) turbulence statistics. The surface or constant stress layer occupies perhaps the 

first 100 m (328 ft) of the atmospheric boundary layer during the day in unstable and neutral 

conditions, but it becomes much shallower in stable nighttime flows. Neither model, then, can 

take into account the influence of buoyancy that we have found so pervasive in shaping the 

temporal and spatial characteristics of turbulence and the subsequent dynamic response of wind 

turbine components. Finally, the very large turbine rotors now becoming the norm reside either 

partially or fully above the height of the SL. This region, which extends to the top of the 

atmospheric boundary layer, is called the mixed layer (ML), and turbulent conditions and their 

scaling can vary significantly from those in the SL. In the ML (also referred as the residual layer 

in stable, nocturnal flows), buoyancy is a major player. We need inflow simulations that reflect 

the reality of turbine operating environments and not idealized ones—this is what TurbSim 

strives to do in an efficient manner. 

Given that TurbSim is an outgrowth of Veers’ original SNLWIND and Kelley’s expansion 

SNLWIND-3D, much of the fundamental basis for the stochastic simulator was discussed in 

Veers (1988) and Kelley (1992), and we encourage the reader to look at those documents. Here 

we concentrate on what has gone into scaling the important features of the turbulence fields 

being simulated by the site-specific spectral models offered by TurbSim and to a limited extent 

how it has been implemented. For information on how to use the code, the reader is referred to 

Jonkman (2009). 

226
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9.2 Important Parameters and Conditions To Be Simulated

The basic process of simulating a realistic full-field flow for the National Wind Technology 

Center (NWTC) and Lamar sites functionally is the same as that followed in Kelley (1992) to 

develop what became SNLWIND-3D. As we pointed out previously, however, one significant 

omission in our initial simulation of the inflows to the two California wind farm Micon 65/13 

turbines was the lack of small-scale coherent turbulent structures. We addressed this issue by 

including such structures in the wind farm models (upwind location [WF_UPW], the flow at 

Row 37 with the upwind 7D turbine spacing [WF_7D], and downwind of Row 41) with the 

nearest operating turbine row 14D upstream (WF_14D). We incorporated this feature in the 

development of the NWTC (NWTCUP) and the Great Plains Low-Level Jet (GP_LLJ) spectral 

models based on our field measurements from each site. 

The California wind farm turbines operated very close to the ground, which allowed us to apply 

SL turbulence scaling exclusively. At the NWTC site, however, at the highest measurement in 

the planar array (58 m), we found that under stable flow conditions SL scaling was breaking 

down; i.e., the shearing stress or local friction velocity u* was becoming a function of height. In 

Lamar the entire depth of the equivalent rotor was well within the ML except during strong 

convection and high surface wind speeds. Earlier we noted the levels of heterogeneity within the 

Advanced Research Turbine (ART) rotor disk at the NWTC and the equivalent heights of the 

virtual WindPACT rotor in Lamar, which violated the equilibrium conditions of SL scaling as 

well. Because there is no universal ML equivalent to SL scaling theory, we applied what can be 

described as an SL-ML hybrid (modified local scaling) approach based on our empirical 

measurements. Velocity and temperature fluctuations in the SL are based on the velocity, 

temperature, and height scaling parameters u , T , and LM-O defined by Equations 2-5, 2-6, and *o *o 

2-7 and measured at the surface. The vertical variation of U(z) in a non-neutral or diabatic 

atmosphere is given by the diabatic log wind profile 

    U (z ) = (u*o / κ) ln	   z + z zo , L O  (9-1)   zo    ψ ( , M − )

where κ is the von Kârmân constant ≈ 0.4, ψ is the diabatic correction term, and zo is a 

characteristic surface roughness length. In developing our empirical scaling equations for the 

various turbulence parameters, we initially used u*, z, and the stability variable z/LM-O averaged 

over the disk layer. 

We found, because of departures from SL theory, many parameters we were trying to scale were 

more highly correlated with RiTL than with z/LM-O. The variable z/LM-O is, however, necessary to 

scale the target velocity frequency spectra to which the inverse Fourier transform process is 

applied to obtain the velocity time series. It therefore was necessary to obtain the variation of 

z/LM-O with RiTL. For the wind farm models, we used a relationship between Ri and z/LMO 

suggested by Panofsky and Dutton (1984), which is based on the Businger-Dyer flux-profile 

relationships (Dutton et al. 1979). This was necessary because the available instrumentation did 

not allow us to directly determine z/LMO. The relationships used for the wind farm models are 

227
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ri for Ri < 0 

z/LMO = Ri/(1-5*Ri) for 0 ≤ Ri < 0.18 (9-2) 

5.616 for Ri ≥ 0.18. 

Businger and coauthors (1971) found that for an unstable (Ri < 0) surface layer over 

homogeneous terrain conditions, setting z/LMO = Ri was a reasonable approximation. For stable 

conditions they found 

z/LMO = (0.74 + 4.7Ri)/(1+4.7Ri) . (9-3) 

It was no surprise that neither of these relationships fit the observed NWTC data given the level 

of intense heterogeneity in part caused by the significant downward momentum and buoyancy 

fluxes common to this site. This was also true at the Lamar site, where the bulk of the 

measurements were taken well above the surface layer and during stable conditions by design. 

These fluxes are similar to those at the NWTC but have low-level jets in the nocturnal boundary 

layer. 

For both sites we correlated the rotor disk layer mean values of the locally measured z/LMO(z) 

values (now referred to as z/LD) with the corresponding RiTL. We found that the variation in z/LD 

fell into three distinct ranges of RiTL, including two unstable classes and one stable class. The 

measured relationships for the NWTC are 

-0.254 + 1.047RiTL for -1 < RiTL ≤ -0.10 

(10.379RiTL)/(1 - 19.393RiTL) for -0.10 < RiTL < 0 

z/LD = (2.535RiTL)/(1 - 6.252RiTL) for 0 ≤ RiTL < 0.155 (9-4) 

12.7 RiTL ≥ 0.155 . 

For the Lamar site we found 

-0.047 + 1.054RiTL for -1 < RiTL ≤ -0.10 

(2.213RiTL)/(1 - 4.698RiTL) for -0.10 < RiTL < 0 

z/LD = (3.132RiTL)/(1 – 6.762RiTL) for 0 ≤ RiTL < 0.137 (9-5) 

5.66 RiTL ≥ 0.137 . 

228
 
 

 

Figure 9-1. Estimated values of rotor disk layer average stability parameter z/LMO as function of 

RiTL. The NWTC and Lamar relationships were empirically determined from direct measurements 

of local values of z/LMO and RiTL at these two sites. The vertical dashed line at RiTL = +0.10 

corresponds to the nominally upper limit of turbine dynamic response seen on the Micon turbines 

and the ART. 

229 
 

 

 

 

 

 

 

 

 

 

We found we could limit the scaled range of z/LD to ± 1. Figure 9-1 compares the variations of 

the estimated values of z/LD as a function of RiTL. 

9.3 TurbSim Independent Scaling Variables

SNLWIND-3D and now TurbSim use only a very limited number of user defined boundary 

conditions or independent variables to scale the simulated full-field turbulence for each of the 

supported spectral models. These include characteristic measures of the following: 

•	 Mean wind speed at a specified height within the rotor disk being modeled 

•	 Velocity shear across the rotor disk 

•	 Turbulence level or intensity 

•	 Dynamic stability of the turbine layer 

•	 Presence of coherent turbulent structures 

• Height and intensity of a low-level jet stream. 

The variables implemented in TurbSim to satisfy these criteria are the: 

•	 Mean wind speed at a specified height within the rotor disk (U at z) 

•	 Power law shear exponent across the rotor disk (α) 

•	 Mean shearing stress or friction velocity over rotor disk layer (u*D ) 

(a specific the turbulence intensity can be used to scale the IEC spectral models) 

•	 RiTL 

•	 Presence and location of coherent turbulent structures within the rotor disk 

• Height and intensity of a low-level jet. 

The turbulence spectral models that have been implemented in TurbSim include: 

•	 The IEC Kaimal model (IECKAI) 

•	 The IEC von Kârmân model (IECVKM) 

• The Risø diabatic homogenous- or smooth-terrain model (SMOOTH). 

The NREL site-specific models include: 

•	 The NREL San Gorgonio wind farm models 

o	 Upwind of Row 1 (WF_UPW) 

o	 Upwind of Row 37 (WF_7D) (7D row-to-row spacing) 

o	 Downwind of Row 41 (WF_14D) (14D row-to-row spacing) 

•	 The NREL NWTC model (NWTCUP) 

230
 
 

 

 

 

 

 

 

 

 

 

 

o KHTEST model (severe but observable implementation of NWTCUP) 

•	 The NREL Great Plains Low-Level Jet Model (GP_LLJ) 

o	 No LLJ present (power law shear profile) 

o	 LLJ jet present (LLJ shear profile) 

o	 Coherent turbulent structures present/not present. 

The choice of including coherent structures in the simulation is available only with the NREL 

site-specific spectral models, and only the GP_LJJ supports low-level jets. So, with the exception 

of the discrete choices, including coherent structures or low-level jets, the scaling of the 

simulated turbulence within the user-defined turbine rotor disk height geometry is accomplished 

by specifying only the U, α, u*D, and LLJ characteristics (if used), and RiTL. The first four 

describe the velocity field and the last introduces the influence of the important vertical variation 

of temperature (buoyancy on the simulated background turbulent wind flow) within the 

simulated rotor disk. As we discuss later, the coherent structures are superimposed on this 

background, much in the same way KHI-induced billows occur in natural flows. 

9.4 Developing Turbulence Scaling for NREL Site-Specific Spectral Models from 

Field Measurements 

We developed the scaling of the predicted turbulence statistics as functions of height (z) across 

the rotor disk of the: 

•	 Turbulent spectral energy distributions S n ui 

() where i= u, v, w turbulent velocity 

component and n is the cyclic frequency in hertz 

•	 Vertical variation of the mean U (and V if the GP_LLJ with a LLJ is specified) 

•	 Temporal coherence via the mean Reynolds stress components, uw ' ', u v' ', and vw ' ' 

•	 Spatial coherence for u, v, and w turbulence components within and extending slightly 

beyond the specified rotor disk diameter to accommodate large yaw and teeter angle 

variations in the subsequent turbine simulations 

•	 Coherent structure characteristics: locations, intensity (peak Ecoh), total length (Tcoh), and 

number (Ncoh) 

•	 The LLJ jet characteristics of height and intensity of the jet maximum velocity when the 

GP_LLJ model is used and if not specifically defined by the user. 

9.4.1 General Analysis and Modeling Procedure

Using the independent variables, we applied multiple-linear regression (MLR) coupled with 

LOESS smoothing to develop empirical scaling models of the target turbulent statistical 

parameter. In one or two instances, a nonlinear transformation of one of the predictor variables 

was included in the MLR model if it would improve the model performance. We examined the 

probability distributions of the residuals after identifying and retaining the most efficient 

predictors to achieve the maximum coefficient of multiple regression statistic R2 as well as other 

measures of goodness-of-fit such as the F-statistic. An additional offset correction was made to 

231
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

the final regression equation if it was found that a significant bias was present in the residuals. If 

the residual probability distribution differed significantly from Gaussian, we fitted it to an 

appropriate parametric model. A random sample from this residual model distribution was then 

added to the MLR model to provide the best estimate of the target scaling parameter with its 

inherent random variability. 

Our two primary independent variables in developing the MLR and associated random models 

are the mean hub-height U wind speed and RiTL. The observed available range of wind speeds 

were first divided into 2-m s–1 categories. The RiTL values were stratified by the stability classes 

STC01, STC02, STC03, STC04, and STC05. The STC03 class included both the critical 

Richardson number range, or CRR, and the CRR High, or CRRH, ranges. In practice the most 

unstable STC01 class (–1 ≤ RiTL ) was not included in the MLR modeling because (1) there were 

so few observations within this range for all three sites and (2) the mean wind speeds were 

typically low and often below cut-in speed. Our first wind speed bin range began at 3 m s–1 , 

which was usually just below cut-in speed for most of the turbine designs, virtual or otherwise, 

discussed here. Typically the combination of available wind speed and stability classes produced 

up to 70 or more statistical degrees of freedom (DOF) in modeling the observed ranges of the 

target parameters for the wind farm, NWTC, and Lamar sites. We performed the stepwise MLR 

procedure for each stability class that contained a statistically significant number of observations 

within each wind speed category. This procedure initially included one or more of the candidate 

predictor variables u*D, the surface u*o, α, z/LD, and the local value of z/L(z), and whether 

coherent structures were present or not. In developing the models with coherent structures 

present, we used only the cases in which these turbulent patches had been detected 

simultaneously at all measurement (sonic anemometer) locations. This ensured that we were 

scaling the potentially most influential situation on turbine dynamic response. We also included 

the jet height and intensity as additional predictor variables when modeling the Lamar site if an 

LLJ had been detected by the sodar below a height of 500 m above ground level (AGL). 

The shearing stress or friction velocity u* is the parameter that scales the turbulence level, as we 

see in our discussion of the spectral energy distributions. For the wind farm sites, we used the 

direct measurements at the equivalent turbine hub heights. At the NWTC, we found that we 

could use the disk-averaged value based on the mean surface stress or u*o computed from 

Equation 9-1. The variation of u*D with u*o was found to be weakly correlated with RiTL and is 

plotted in Figure 9-2a. A random correction to Figure 9-2a is plotted in Figure 9-2b, and the final 

value of u*D is estimated in TurbSim as 

u*D = u*o + 0.205 – 0.0101Uhub + 0.00904RiTL + RANDOM contribution . (9-6) 

The same approach is taken to estimate a disk-averaged value of z/LD by Equation 9-1 and 

random adjustment from the probability distribution in Figure 9-3: 

z/LD = z/Lo – 0.247 + 0.0188Uhub – 0.251RiTL + RANDOM contribution . (9-7) 

232
 
Figure 9-2. (a) Variation of NWTC ART rotor disk average value of local u* (u*D) with diabatic 

surface value, u*o; (b) probability density distribution of u*D – u*o 

233 
 

Figure 9-3. Probability density function of z/LD – z/Lo difference for NWTC ART rotor disk 

234 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

For the Lamar site we found u*D to be 

u*D = 0.0702 + 0.0249U85 – 0.0473RiTL , (9-8) 

where U is the mean speed at the 85-m (hub) height. 

The variation of u*D with u*o for the Lamar site is plotted in Figure 9-4 for (1) all observations, 

(2) those with coherent structures at all heights, and (3) no coherent structures at any height. A 

best fit curve for all of the cases is also plotted. Figure 9-5 plots the observed variation of the 

local values of the stability parameter z/L(z) at the four measurement heights on the tower with 

the surface value z/Lo. The largest difference occurs at the 116-m level, which is well into the 

ML. We also included the variation of the disk layer mean z/LD shown as the blue-white dashed 

line. These curves show the level of decoupling near the surface and with the increasing 

penetration into the ML. 

9.4.2 Modeling the Turbulent Spectral Energy Distributions

We applied the procedures discussed in Kelley (1992) to the NWTC and Lamar data that we 

used to derive the spectral scaling of the three turbulent velocity components 

v S () at the three locations within the California wind farm. For stable SL u ( ), nSn( ), and Sw n 

scaling 

nS n L ) , (9-9) i ( )/ u*

2 = F( f , z / M O−

and for unstable scaling 

nSi ( )/ u*

2 

n = F( f , zi ) , (9-10) 

where i = u, v, and w; n is the cyclic frequency; f is the reduced frequency given by nz/U; and zi 

is the mixed layer depth. We estimate zi using the relationships derived from Dutton, et al. 

(1979) and ESDU (1993) 

400U 

 z  for u* < u*o 

log 10  
  zo 
 

zi = , (9-11) 

u* for u ≥u , * *o 6 fc 

where U is the mean wind speed at height z, zo the surface roughness length, u*o is the surface 

value of u*, , and fc is the Coriolis parameter 2ω sin(Ω), with ω being the Earth’s rotation rate 

and Ω the latitude. 

235
 
Figure 9-4. Variation of rotor disk layer mean value u*D with surface value u*o for all cases (black 

line), with coherent structures at all heights (red line), and with no coherent structures at any 

height within rotor disk layer (white dashed line). The dashed blue line is the best fit curve for all 

cases. 

236 
 

Figure 9-5. Lamar site variation of local stability parameter z/L and z/LD with z/Lo by height. 

Horizontal and vertical dashed lines outline observed z/L value range of 1. 

237 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

We used the Risø SL spectral models (Højstrup 1982; Olesen, Larsen, and Højstrup 1984) for 

unstable and stable flows as the basis spectrum description and derived empirical scaling ratios 

Ψ, Φ to adjust the amplitudes and positions of the spectral peaks to agree with the site-specific 

measurements. For flat, homogeneous terrain, Kaimal and Finnigan (1984) and Kaimal et al. 

(1972) found that the u and v turbulent spectra in unstable flows could be modeled as the sum of 

two spectral peaks, as follows: 

L n H S n() = S () + S n () , (9-12) 

where SL(n) and SH(n) are independent low- and high-frequency spectral contributions from 

turbulent kinetic energy created by buoyancy and shear, respectively. They found that the 

vertical velocity spectrum Sw(n) had only a single peak. We found in analyzing the field data 

from the California wind farm, NWTC, and Lamar sites that multiple peaks existed in the u and v 

components for stable as well as unstable flows, probably from the influence of the mountainous 

terrain upstream, including Colorado. We also identified the existence of low- and highfrequency peaks in the vertical wind component in all except the Lamar site. Again this was 

probably related to the upstream mountainous terrain in San Gorgonio and at the NWTC. 

To resolve these low frequency spectral peaks, we extended the length of the records to 30 

minutes by concatenating contiguous triplets of 10-minute records that were at least quasistationary based on their second statistical moments. The amplitude and position of the spectral 

peaks were identified in each of these expanded records. We stratified the resulting spectral 

peaks by first stability class and then wind speed class. Empirical relationships with boundary 

turbulent scaling parameters and the spectral scaling ratios Ψ and Φ were then obtained for the 

low- and high-frequency peaks in each of the stability and wind speed classes. The same 

procedure was employed in analyzing the turbulence measurements from the NWTC and Lamar 

sites using the STC02, STC03, STC04, and STC05 stability classes and each of the 2-m s

–1 mean 

wind speed categories appropriate for the particular site. 

Figures 9-6 and 9-7 display the resolved low- and high-range spectral peaks found upwind of 

Row 1 and downwind of Row 41 in the wind farm as a function of RiTL. Figure 9-6 shows the 

cyclic frequencies associated with spectral peaks for each of the turbulent wind components. The 

1/rev rotor rpm rates are indicated by the horizontal dashed lines. The same format is followed in 

Figure 9-7, but the peaks are presented as wavelengths scaled as equivalent rotor diameters for 

rated wind speed conditions. We were able to identify two spectral peaks for the vertical wind 

component in stable flows that were not found by Kaimal and Finnigan (1994), Kaimal and 

coauthors (1972), or Olesen and coauthors (1984) over flat, homogeneous terrain. The IEC 

Kaimal NTM equivalents are shown in both figures for neutral stability conditions. There is 

reasonable agreement with the observed u-component peaks, but significant deviations exist both 

upwind and downwind in the v- and w-components with the IEC Kaimal NTM. Figure 9-7 shows 

that spectral peaks in these components are much smaller than the rotor disks but at least one of 

the observed peaks is very close to coinciding. 

238
 
 

Figure 9-6. Variations of resolved turbulence high and low cyclic frequency spectral peaks upwind 

of Row 1 and downwind of Row 41 of California wind farm environment with Micon 65/13 RiTL. 

Horizontal dashed line represents 1/rev cyclic frequency. The CRR and CRRH stability class 

boundaries are shown as vertical dashed and dotted lines, respectively. 

239 
 

Figure 9-7. Same as Figure 9-6, but spectral peaks are scaled with equivalent Micon 65/13 rotor 

diameter for rated wind speed conditions 

240 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figures 9-8 and 9-9 show the resolved low- and high-range spectral peaks found for the NWTC 

ART and the virtual WindPACT turbine operating in the Lamar site environment using the same 

format. In agreement with Kaimal et al. (1972) and Olesen et al. (1984), the Lamar site vertical 

turbulence component exhibits the single spectral peak characteristic of flat, homogeneous 

terrain. Flow at the NWTC, however, like the wind farm, contains both low- and high-frequency 

peaks. We believe this is a consequence of the mountainous terrain upwind of both sites. This 

signals a significant difference in the flow conditions that turbines are exposed to that is not 

replicated in the IEC Kaimal neutral NTM. Under neutral conditions, there is reasonable 

agreement in the u-component peak between the IEC Kaimal NTM and the observed peaks at the 

NWTC and Lamar sites. Much larger variances exist for the v- and w-components, however, 

which is consistent with our earlier observations of the greater levels of turbulent energy in these 

lateral components and again a likely consequence of the nearby complex terrain. Looking at the 

both the upwind and downwind San Gorgonio data in Figure 9-7 that falls within the CRR 

stability class (+0.01 ≤ RiTL < +0.05), we see that the short (high-frequency) and v- and wcomponent wavelength peaks occur very near the rotor diameter. The NWTC w-component short 

and long wavelength peaks in this same stability range closely bracket the equivalent rotor 

diameter. These peaks in the vertical component of turbulent energy in this critical stability range 

could easily be manifestations of Kelvin-Helmholtz Instability (KHI), and having scales closer to 

the rotor diameter could easily reflect a buoyancy length scale Lb near the same dimension since 

Lb ∝ σw by definition. We previously demonstrated that enhanced turbine dynamic response 

occurs when Lb ≈ D. 

The target frequency low- and high-frequency range spectra were arrived at by scaling the Risø 

SL models (Højstrup 1982; Olesen, Larsen, and Højstrup 1984) with the amplitude and 

positional scaling factors Ψ and Φ, respectively, which are empirical functions of u* and z/LM-O 

derived for each of the wind speed and RiTL ranges. The source of the u* and z/L scaling 

parameters varies with the site. For the wind farm models, the hub-height measured value of u* 

was used and the z/L stability parameter was derived from RiTL using Equation 9-2. The neutral 

and stable NWTC model (NWTCUP) scaling factors Ψ and Φ use only the measured turbine 

layer mean z/L or z/LD, but for the unstable spectra they depend on both the turbine layer mean 

values of u*D and z/LD. For the Lamar site, in the GP_LLJ we apply local scaling because the 

atmospheric layer of interest is well within the ML. Here Ψ and Φ are functions of height within 

a given wind speed and stability classification and we use empirical relationships based on the 

locally measured values of u* (z) and z/L (z) for both unstable and stable turbine layer conditions. 

Figure 9-10 given examples of the wind farm spectra for the same hub wind speed and u* value, 

but for RiTL values of –0.05, 0, and +0.05. The spectral distributions for the WF-07D and WF14D spectral models inside the wind farm are the same and overlap. The u-component spectra 

show a larger contribution of low-frequency streamwise energy that increases with stability 

upwind of the wind farm. The lateral components v and w show a general increase in turbulent 

energy with increasing stability. Figures 9-11a and 9-11b plot similar information for the 

NWTCUP and GP_LLJ models, respectively. The NWTC site has a greater contribution of low 

frequency turbulent energy in the u and v components downwind of mountainous terrain 

compared with that seen in the flatter and more homogenous terrain associated with the Lamar 

site. The spectral distributions associated with the eight 

241
 
 

Figure 9-8. Same as Figure 9-6, but for NWTC ART and virtual WindPACT turbine in Lamar site 

environment 

242 
 

Figure 9-9. Same as Figure 9-8, but spectral peaks are scaled in equivalent rotor diameters for 

rated wind speed conditions 

243 
Figure 9-10. Example of turbulent component logarithmic spectral variations with stability for wind 

farm models (WF_UPW, WF_7D, and WF_14D). The WF_7D model uses the same spectral 

distribution as the WF_14D model, and therefore the plotted spectra for these two positions in the 

wind farm are identical because a common value of u* was used to scale all three models. 

244 
 

 

Figure 9-11. Comparison of variation of turbulent component logarithmic frequency spectra with 

stability for hub height of 80 m, Uhub = 15 m s–1, and u*D = 1.1 m s–1 for (a) NWTCUP and (b) GP_LLJ 

models 

models available in TurbSim are summarized in Figure 9-12 for a hub height of 80 m, mean 

wind speed of 15 m s–1, and a turbine layer mean u*D value of 1.1 m s–1 by RiTL values of –0.05, 

0, and +0.05 in columns (a), (b), and (c). The grey shaded areas outline the IEC Kaimal 

(IECKAI) NTM and the light blue line with the x-symbol the IEC von Kârmân (IECVKM) 

neutral spectral models. The largest obvious deviation from the IECKAI model is the energy in 

the w-component spectra, which generally increases with increasing stability. 

In Figure 9-13 we plot the variation with stability of the equivalent wavelengths (space scales) of 

the high-frequency spectral peaks of the turbulence components found at the 23-m hub height 

downwind of the wind farm. The rotor diameters of the NREL and AeroStar rotors are shown as 

245 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

horizontal solid and dashed lines, respectively. The CRR stability range is annotated with the 

vertical dot-dot-dashed line within its boundaries as the value of RiTL where we found the 

maximum dynamic response of the Micon 65/13 turbines. Clearly the wavelengths of these 

spectral peaks coincide with the rotor diameters within the CRR stability range, and the vertical 

component peak also coincides closely with the RiTL of the maximum turbine dynamic response. 

In Figure 9-14a we compare the ratios of the hub-height turbulence components u, v, and w with 

the local value of u* and σ σ/ and σ σ/ upwind of the wind farm Row 1 for stable v u w u 

conditions, and Figure 9-14b contains the same information for downwind of Row 41. 

We know from our previous discussion that the CRR range is dominated by the fastest-growing 

turbulent structures created by KHI, and their equivalent dimensions are similar to the turbine 

rotor disk diameters. The strong correlation between the Micon turbine dynamic loads and the 

σ σ/ and σ σ/ ratios is pictured in Figure 3-17. We are assured thus that the TurbSim WF- v u w u 

07D and WF-14D spectral models reproduce this aspect of wind farm internal background wake 

flows. We also know, however, that the most intense coherent structures are not included in this 

flow and must be introduced by other means. These results also underscore the fact that the 

nature of internal wake flows within a large wind farm is heavily influenced by KHI, which must 

be included in any microscale simulations of such phenomena. The need to include KHI is 

further supported by comparing Figure 9-14a (WF_UPW) and the modeled conditions by over 

flat, homogenous terrain (Risø SMOOTH model) and downwind of complex terrain at the 

NWTC (NWTCUP model) in Figure 9-15. In Figures 9-14 and 9-15 we see that the models 

simulating flows near mountainous complex terrain have similar characteristics, but conditions in 

smooth, homogenous terrain are significantly different. The IECKAI is approximately equivalent 

to a neutral scaling of the TurbSim implementation of the Risø SMOOTH spectral model. The 

turbulent conditions within the wind farm in Figure 9-14b are, however, even more disparate 

compared with the others. We are seeing the effects of an atmospheric resonance created by K-H 

instability that occurs with such frequency as to influence the background flow within the wind 

farm under weakly stable conditions (CRR and CRRH stability ranges). Such conditions occur 

outside of the wind farm but much less frequently, as hinted at by the σw /u* ratio peaks 

occurring within the CRR stability range in the SMOOTH and NWTCUP models in Figure 9-15. 

246
 
Figure 9-12. Comparisons of TurbSim model turbulent component spectra for hub height of 80 m,
 

Uhub = 15 m s–1, u*D = 1.1 m s–1: (a) RiTL = –0.05; (b) RiTL = 0; (c) RiTL = +0.05
 

247 
Figure 9-13. Variations of equivalent wavelengths of high-frequency turbulence component 

spectral peaks with RiTL. San Gorgonio WF_7D and WF_14D spectral models scaled with the hub 

height of 23 m, Uhub = 12 m s–1, and u* = 1 m s–1. 

248 
 

Figure 9-14. California wind farm variations of ratios of u , v , and w with hub u* and v /u , w 

/u with stable stability for (a) upwind of Row 1; and (b) upwind of Row 37 (7D) and downwind of 

Row 41 (14D) 

249 
Figure 9-15. Variation of ratios of u , v , and w with hub u* and v /u , w /u with stable stability 

for (a) TurbSim SMOOTH and (b) NWTCUP spectral models 

250 
 

 

 

 

 

 

 

 

 

 

 

 

 

9.4.3 Cross-Component Correlation and Mean Reynolds Stress Component 

Scaling

We demonstrated the importance of coherent turbulence in the dynamic response of wind 

turbines. Turbine blade root damage equivalent and peak loads were shown to scale with 

coherent kinetic turbulent energy or Ecoh (CTKE), which defined as the magnitude of the vector 

sum of the Reynolds stress components uw uv ' , ' ' ' , and ' vw ' . These components are measures of 

the degree of cross correlation between the orthogonal turbulence velocity components u, v, and 

w that exists in the background flow over a 10-minute record. Figure 9-16 summarizes the 

probability distributions of the cross-correlation coefficients r r uw, uv , and rvw for the available 

unstratified populations from hub height at the three wind farm locations and the available 

measurement heights at the NWTC and Lamar sites. These plots reveal that the local background 

flow velocity components at all three sites and heights, with perhaps one exception, have a 

significant level of correlation and therefore nonzero Reynolds stress components. The flows 

upstream, within, and downstream of the multirow wind farm have narrower distributions than 

the purely natural flows seen at the NWTC and Lamar sites. So it is important that flows 

simulated by TurbSim reproduce these turbulence correlation characteristics at the three sites. 

By design, the Fourier inversion process creates a velocity time series with random phase from 

the target frequency spectrum. Cross-component characteristics must be introduced into the 

simulated time series to reproduce the correlation or phase distributions seen in Figure 9-16. This 

is accomplished by specifying target mean Reynolds stress components at the hub height of the 

turbine being modeled. We developed MLR models of the variation of these mean stresses as the 

dependent variable and the available input scaling parameters as the independent variables. Table 

9-1 lists the parameters with a statistically significant influence on the three hub-height mean 

Reynolds stress components for the three locations at the wind farm. It is interesting to note that 

stability was not one of the parameters. Tables 9-2 and 9-3 present the sensitivity matrices for the 

available measurement heights at the NWTC and Lamar sites. Height relationships were then 

developed to scale these independent variables to define vertical variation of the magnitudes of 

the mean Reynolds stress components across the height of the disk layer. 

These models produce only estimates of the mean stress components and do not include their 

polarity. In Figure 9-17 we plot the residuals from the hub-height MLR fits, which provide the 

polarity distribution about the mean. These can be described as a bias plus a random component. 

As an example, the residuals from the uw ' ' MLR model for the internal San Gorgonio sites 

(Figure 9-17a) at Rows 37 and 41 have a substantial negative bias because of the strong 

downward momentum fluxes discussed earlier. The equivalent Gaussian distribution fits are 

shown with dashed lines. All three of the random distributions follow Gaussian distributions 

closely. The u v' and ' v w' 'components exhibit much smaller or near zero biases and also are 

Gaussian distributed, but the variability (breadth) varies considerably with the 7D upwind rowto-row spacing conditions at Row 37 creating the greatest variability in the u v' 'mean stress. 

With the exception of the u v' 'stress, the residual distributions from the natural inflows at hub 

height at the NWTC and Lamar sites (Figures 9-17b, c) have zero or very small biases but 

generally non-Gaussian distributions. The u v' 'stress distributions have very long negative tails. 

The negative tail at the NWTC extends 10 times greater than that at the Lamar site. We 

implemented the target mean Reynolds stress components in TurbSim derived from the sitespecific MLR model plus a random component whose probability distribution is particular to the 

251
 
 

site and stress component. Figures 9-16 and 9-17 show the significant variation between the 

sites, particularly for the u v' and ' v w' 'stress (correlation) levels, none of which is included in 

the IEC Kaimal NTM or von Kârmân spectral models. The neutral IEC Mann constant stress 

model includes the full Reynolds stress tensor or components, but it is not clear if it would 

reproduce the contents of Figure 9-17. It seems doubtful since these distributions are empirical 

and site specific. We saw in Figures 3-17 and 3-18 for the Micon turbines and Figure 4-23 the 

ART that root bending fatigue damage and peak loads are very sensitive to the level of these two 

mean Reynolds stress components in the CRR stability range. The Micon low-speed shaft 

dynamic response is also very sensitive to the v w' ' component within the same stability range, as 

is shown in Figure 3-23. Clearly, simulating these mean stress distributions is very important to 

fully induce the dynamic loading seen in actual turbine operations in these environments! 

252
 
Figure 9-16. Observed turbulence component cross-correlation coefficient probability distributions (ruw, ruv, and rv

at three locations at California wind farm, three heights within ART rotor disk on Row 4 of NWTC, and at five he

WindPACT 1.5-MW turbine rotor disk layer at Lamar site 

253 
 

 

Table 9-1. Mean Reynolds Stress Scaling Magnitudes Sensitivities at California Wind Farm Locations with 

Turbine Layer Turbulence Parameters
 

uw ' ' component 

Location Uhub U D ∂ / ∂z

2 

* hub u 

Upwind (Row 1)  

7D (Row 37)  

14D (Row 41) 

uv ' ' component 

Upwind (Row 1)  

7D (Row 37) 

14D (Row 41) 

vw ' ' component 

Upwind (Row 1)  

7D (Row 37) 

14D (Row 41) 

254
 
 

 

Table 9-2. Sensitivities of Mean Reynolds Stress Component Magnitudes to Turbine Layer Turbulence 

Scaling Parameters in NWTC Row 4
 

z Uhub RiTL u* 

2 

D D ( ∂U / ) ∂z z/LD 

uw ' ' component 

58 m    

37 m    

15 m  

uv ' ' component 

58 m    

37 m    

15 m  

vw ' ' component 

58 m     

37 m    

15 m  

255
 
 

 

Table 9-3. Sensitivities of Mean Reynolds Stresses Magnitudes to Turbine Layer Turbulence Scaling
 

Parameters at Lamar Site
 

z Uhub RiTL z/LD U D ∂ / ∂z u* 

2 

D 

uw ' ' component 

116 m     

85 m    

67 m    

54 m   

uv ' ' component 

116 m   

85 m   

67 m   

54 m   

vw ' ' component 

116 m    

85 m    

67 m    

54 m    

256
 
Figure 9-17. Available population Reynolds stress component residual distributions for hub heights at (a) wind f

Lamar site (virtual WindPACT 1.5-MW turbine). Dashed lines represent the Gaussian distributions for the observed 

257 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9.4.4 Spatial Coherence Scaling

The coherence function for the wind farm (WF_UPW, WF_07D, and WF_14D), the NWTC 

(NWTCUP), and the Great Plains (GP_LLJ) spectral models is given by 

 2   fr  2

Coh = exp −a + (b r )  , (9-12) ij , κ κ   κ   um    

where κ is the turbulence component u, v, or w; f is the cyclic frequency; r is the distance 

between points i and j; zm is the mean height of the two points; and um is the mean wind speed 

over the entire simulation. It is based on the form suggested by Thresher et al. (1981) where a 

and b are the coherence decrement and offset parameters. We analyzed the “a” decrement and 

offset “b” terms as functions of wind speed and stability for the wind farm, NWTC, and Lamar 

sites. In the wind farm we found them to vary only with mean wind speed. At the NWTC and 

Lamar sites, however, we found that although they were generally most sensitive to wind speed, 

the u and v components did also vary with the stability class (STC01, STC02, STC03, STC04, 

and STC05), with the vertical component w somewhat less so. 

In Figure 9-18 we compare the NWTC and Lamar site variations of the decrements aκ as a 

function of height and RiTL for hub-height mean wind speeds in the 12–14 m s–1 range. In 

general, for both sites the horizontal velocity decrements au and av increase with increasing 

stability, whereas the vertical decrement aw reaches a minimum under neutral to slightly stable 

conditions and maximum when it becomes very unstable or very stable. The variations of the u, 

v, and w decrements (aκ) and offsets (bk) with mean wind speed for each of the available stability 

classes are plotted in Figures 9-19, 9-20, and 9-21, respectively, for the NWTC and Lamar sites. 

Figure 9-19 plots the IEC values for the u-component from IEC (1999; 2005). The v and w 

decrements and offsets are not specified by the standard. Figure 9-22 plots the variations in these 

parameters for the u and v components in the wind farm in a similar format. These values are 

based on cup anemometer data because sonic anemometers were available only at a single height 

and so there is no measurement of the w-component and its coherent scaling parameters. In 

applying these data we assumed that the coherence conditions are similar at Rows 37 and 41 and 

that aw ≈ au and bw ≈ bu. 

258
 
Figure 9-18. Variation of coherent decrement “a” with height and RiTL for mean wind speed range 

of 12–14 m s–1 for (a) NWTC ART and (b) Lamar site (WindPACT 1.5-MW turbine) 

259 
 

 

Figure 9-19. Variation of U-component coherence decrement “a” and offset term “b” normalized 

by Lu integral length scale by stability class and hub mean wind speed: (a) NWTC ART and (b) 

Lamar site (WindPACT 1.5-MW reference turbine) 

260 
 

Figure 9-20. Same as Figure 9-19, but for V-component 

261 
 

Figure 9-21. Same as Figure 9-19, but for W-component 

262 
 

Figure 9-22. Variation of U- and V-component coherence decrement “a” and b offset term 

normalized by integral length scale L for California wind farm upwind of Row 1 and at Rows 37 

and 41. Vertical component coherence scaling was unavailable because of a lack of vertical 

velocity measurements. 

263 
 

 

 

 

 

 

 

 

 

 

 

9.4.5 Coherent Structure Scaling and Implementation

In Section 6 we discussed the role of coherent turbulent structures in the dynamic response of 

wind turbines. We saw that these structures, because of the nature of the KHI that creates them, 

are superimposed on the background flow from which they derive their energy. We pointed out 

that KHI is a highly nonlinear process that cannot be fully reproduced by the linear inverse 

Fourier transformation used in TurbSim to produce the simulated velocity field from target 

frequency spectra. We found that the random occurrence of these structures is non-homogeneous 

Poisson distributed which can be used to describe the time between coherent events (interarrival 

times). These structures also exhibit random intensities defined by the peak values of Ecoh within 

a 10-minute record as well as their number and total or aggregate length. Figure 9-23 shows the 

key elements of a stable, sheared flow containing superimposed coherent structures created by 

KHI. In Figure 9-23a we reproduce the specially processed NOAA HRDL lidar “stare” 

observation from Figure 8-13a, but also include the corresponding mean U velocities at the 

heights measured by the met tower that agree well with the lidar-derived mean wind profile. The 

details of some of the structures seen by the lidar for the subperiod of 330 to 480 seconds are 

plotted as the time series of the Reynolds stress components and their vector magnitude Ecoh in 

Figure 9-23b. The salient points from these figures follow: 

•	 Existence of the intense vertical mean shear in a stably stratified layer 

•	 Presence of coherent structures principally within the lower, more intense shear layer 

•	 Variation of intensity of the coherent structures as indicated by both the lidar and 

corresponding tower measurements
 

•	 Random temporal variation in the uw ' ', u v' ', and ' ' vw 
 Reynolds stress components seen in 

each of the structures in the expanded record of Figure 9-23b
 

•	 Random occurrence and time between structures at a given height 

•	 Existence of periods when coherent structures occur continuously across the depth of the 

shear layer (between 420 and 430 seconds). 

The scaling of the occurrence and intensity of coherent structures superimposed on a mean, 

stably-stratified background shear flow such as seen in Figure 9-23a must thus include the 

random variation within the simulated Y-Z plane of the following: 

1.	 Total length of coherent structures within a simulated record (typically 10 minutes) (Tcoh) 

2.	 Energy intensity of the structures (peak Ecoh) 

3.	 Period of time between the arrival of individual structures (IAT) 

4.	 3-D distribution of the internal velocity fields that are spatially and temporally correlated. 

264
 
Figure 9-23. Same nomenclature as Figures 8-13a and 8-14 of (a) specially processed HRDL lidar 

“stare” observation with tower-measured Ecoh in lower panel; and (b) corresponding towermeasured time series for subperiod of 330–480 seconds of Reynolds stress components and Ecoh. 

Individual (a–f) and regions (g) of coherent structures are outlined by the dotted lines. 

265 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

To accomplish items (1), (2), and (3) for the TurbSim simulation spectral models simulating 

turbulence conditions, we applied the coherent flow characterizations peak Ecoh, Tcoh, and IAT 

measured at the wind farm, NWTC, and Lamar sites discussed in Section 7-6. To improve our 

scaling correlations, we chose to restrict the scaling of the flow characterization parameters to 

only those observations in which coherent structures were occurring simultaneously at all 

available measurement locations. These included the sonic anemometers at the five locations 

within the NWTC ART upwind planar array and the four heights on the Lamar met tower. Only 

hub-height data are available at the three locations within the wind farm. The distributions of 

RiTL and the hub-height mean wind speeds for these subsets are plotted in Figure 9-24. The most 

prevalent value of RiTL for such conditions falls within the CRR stability range. The distributions 

of the rotor disk mean shearing stresses u*D and vertical shear ∂U / ∂z scaling parameters are  D 

plotted in Figures 9-25a and b and 9-25c and d. The median of the NWTC u*D distribution is 

about 20% higher and has much larger high value tail than seen at the Lamar site. The situation 

would, however, be reversed for the mean shear across a WindPACT turbine rotor disk installed 

in Lamar that is most likely a consequence of the frequent occurrence of LLJs. 

The total expected length of coherent structures within a 10-minute record (Tcoh) was found not 

to scale directly with any of the turbulence parameters but could be modeled as a probability 

distribution specific to a given site, listed in Table 9-4. We found, for example, that a single 

model plotted in Figure 9-26 was appropriate for the hub height at all three locations within the 

wind farm. Individual probability models developed for the NWTC and Lamar sites are also 

functions of height within the simulated rotor disks. 

The expected value of the maximum coherent structure energy intensity (peak Ecoh) within a 10­

minute record is scaled in terms of turbulence parameters but the Row 37 (WF_07D), NWTC, 

and Lamar sites also include a random component. Table 9-5 summarizes the scaling sensitivities 

of the turbulence parameters for the TurbSim spectral models. The parameters 

ubc ,σ , and ∆ub refer to the center mean u velocity, standard deviation of the vertical velocity, wbc 

and u-velocity difference (shear), respectively, across the simulated coherent structure (K-H 

billow). The scaling parameters and random contribution are also functions of height for the 

Lamar site. 

The time between coherent structures (interarrival time, or IAT) is the reciprocal of the Poisson 

rate parameter λ. Table 9-6 summarizes the IAT scaling parameter sensitivities. We found for the 

wind farm and NWTC sites it systematically varies with RiTL and u bc at the center of the 

simulated coherent structure or K-H billow. For the Lamar site, we found it was not stability 

sensitive but was a function of height. 

Coherent structures are added to the ut ( ), vt ( ), and w t() background flow turbulence components 

in the Y-Z grid. TurbSim randomly chooses between the available population of 16 contiguous 

nondimensional coherent structures isolated from the NCAR LES stationary K-H billow 

simulation (Kelley et al. 2004) or from the 11 structures extracted by Werne from the Colorado 

Research Associates (CoRA) DNS K-H billow simulation by Werne and Fritts (1999). It does 

266
 
 

Figure 9-24. Observed probability distributions of turbulence scaling parameters associated with 

coherent turbulent structures occurring simultaneously at all available measurement locations for 

ART upwind planar array and Lamar site 120-m met tower. The distributions of RiTL are shown in 

(a) NWTC and (b) Lamar. The distributions of the equivalent hub-height mean U speed are plotted 

in (c) NWTC and (d) Lamar. 

267 
 

Figure 9-25. Same as for Figure 9-24, but for rotor disk mean shear stress u*D: (a) NWTC and (b) 

Lamar; and rotor layer mean shear U / z across respective ART and WindPACT rotor  D 

diameters: (c) NWTC and (d) Lamar 

268 
Table 9-4. Scaling of Expected Length of Coherent Structures (Tcoh) within a Simulated Record by Location 

Location Spectral 

Model 

Scaling 

Source 

Coherent 

Structure 

height (z) 

California Wind Farm Upwind of 

Row 1 WF_UPW WF Random Model 

California Wind Farm Upwind of 

Row 37 WF_07D WF Random 

Model 

California Wind Farm Downwind 

of Row 41 WF_14D WF Random 

Model 

NWTC Row 4 NWTCUP 

NWTC 

Random 

Model 



Lamar Site (LLLJP) GP_LLJ 

GP_LLJ 

Random 

Model 



Figure 9-26. Probability density distribution of observed Tcoh at hub height for the wind farm 

measurement locations within the California wind farm 

269 
 

 

 

 

 

 

Table 9-5. Coherent Structures Maximum Intensity (Peak Ecoh) Scaling Parameter Sensitivities by Location 

Location Spectral 

Model RiTL bc u u*D ∆u b

wbc σ Height 

(z) 

Random 

Component? 

California 

Wind Farm 

Upwind of 

Row 1 

WF_UPW     No 

California 

Wind Farm 

Upwind of 

Row 37 

WF_07D    Yes 

California 

Wind Farm 

Downwind of 

Row 41 

WF_14D    No 

NWTC Row 4 NWTCUP    Yes 

Lamar Site 

(LLLJP) GP_LLJ     Yes 

Table 9-6. Coherent Structures Interarrival Time (1/λ) Scaling Parameter Sensitivities by Location 

Location Spectral 

Model RiTL ubc 

Height 

(z) 

California Wind Farm Upwind of 

Row 1 WF_UPW  

California Wind Farm Upwind of 

Row 37 WF_07D  

California Wind Farm Downwind of 

Row 41 WF_14D  

NWTC Row 4 NWTCUP  

Lamar Site (LLLJP) GP_LLJ  

270
 
 

 

 

 

 

 

 

 

not mix the sources of these structures. Dimensions are then applied to these structures based on 

the boundary conditions of the simulation to obtain fluctuating (zero mean) velocity components. 

This scaling includes the depth and location of the layer containing the billow within the 

simulated rotor disk, the velocity difference (shear) across it, and the billow center mean wind 

speed. The rotor disk layer is used as the default billow depth, though the user can redefine that. 

Realizations of the expected total length of coherent structures (Tcoh) and the peak value of Ecoh 

are derived from appropriate entries in Tables 9-4 and 9-5, respectively, for the spectral model 

being simulated. A sample realization of arrival times is derived from the Poisson distribution 

based on the rate parameter λ = (1/IAT) that has been scaled with the appropriate parameters in 

Table 9-6. Samples from the available populations of dimensionalized coherent structures whose 

peak intensities have been randomly chosen based on Table 9-5 are summed until their aggregate 

length approximates Tcoh or reaches maximum length of the requested record. These requested 

records are typically slightly more than 10 minutes to accommodate the requirements of the 

turbine dynamic simulation codes. Each coherent structure velocity component is added to the 

background components at each grid point in the time domain. 

Figure 9-27 shows an example of the background and coherent structure superposition and 

summation process at a single grid point. The upper three time series plot the background 

streamwise (U), crosswind or lateral (V), and vertical (W) wind components in black and the 

fluctuating (zero mean) coherent structure velocity components ( uv ′ ′ , , and w′) are depicted in 

red. The bottom panel shows the corresponding Ecoh values for the background and with the 

coherent structure velocity components included. Although some of the structures in the 

background exceed the significant threshold limit, the presence of the coherent structure is much 

more damaging, particularly at about 340 seconds into the record. Figure 9-28 gives a similar 

presentation. Here again the background flow contains at least two significant coherent events, 

but adding coherent structures increases it to at least three and possibly four that also more 

intense and damaging. 

271
 
Figure 9-27. Example of background (U, V, W) plus added coherent structure wind components (u', 

v', and w'): streamwise (U + u'), crosswind (V + v'), and vertical (W + w') at specific grid point 

location 

Figure 9-28. Example of a TurbSim NWTCUP spectral model simulation with and without coherent 

turbulent structures (CS) added. Light gray shows significant (~450 seconds) but fewer CS 

generated within the background flow compared with the CS added (~90 seconds). 

272 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9.4.6 Lamar Site LLJ Wind Speed and Direction Profile Scaling

Including vertical profiles of wind speed and direction in the TurbSim GP_LLJ spectral model is 

crucial in simulating turbulence conditions encountered in the Great Plains. As we previously 

discussed, a midrange sodar at the Lamar site measured the 10-minute mean vertical profiles 

from 40 to 500 m in 10-m increments from May to November 2002, as well as during the 2-week 

period in September 2003 when the NOAA HRDL lidar was deployed. A total of 31,774 tenminute raw profiles were obtained during those periods, of which 29,244, or 92%, were usable 

for further analysis. Each profile was analyzed for the existence of LLJs. When identified, only 

the lowest altitude jets were retained. This process resulted in 4,466 profiles that contained jets, 

which is about 16 % of the available usable records. 

The profiles were then processed in the following sequence: 

1.	 Contiguous vertical profiles of speed and direction were formed from the raw data. 

2.	 Each of the contiguous wind speed and direction profiles was fitted recursively with a 

Chebyshev polynomial up to 10th order and the resulting coefficients were retained. 

3.	 The profile Chebyshev coefficient vectors were matched with the corresponding RiTL and 

the local values of U(z), z/L(z), u*(z), σU(z), and σw(z) from the met tower. 

4.	 The wind speed profiles from the surface to the lowest sodar measurement height were 

estimated using the diabatic wind profile and available tower measurements and the 

Chebyshev-smoothed profiles from 40 to 60 m. The wind direction profile was estimated 

using a generalized least square procedure. 

5.	 The resulting Chebyshev coefficient vectors of wind speed and direction and 

corresponding tower parameters were stratified by jet height in 20-m increments from 80 

to 480 m. 

6.	 MLR models were calculated for each of these height-stratified subpopulations using the 

tower measurements or derivatives as the independent variables and the Chebyshev 

coefficients as the dependent variables. 

Figure 9-29 plots the probability distributions of the time of day and the wind direction and 

speed of the jets within each 20-m height bin by the stability classes STC02, STC03, STC04, and 

STC05. We previously established that the STC03 stability class is potentially the most 

damaging to wind turbines. Here we see in Figure 9-29a that LLJs below 120 m and within the 

turbine rotor disk occur in the early evening hours local time, but those above about 150 m 

generally appear near midnight. Figures 9-29b and c show that strongest jets appear at 200 m and 

above within a very narrow southerly wind direction range. Figure 9-30 presents the distributions 

of the corresponding tower measurements of the rotor disk layer mean values of the MoninObukhov stability parameter z/LD in Figure 9-30a, the shearing stress u*D in Figure 9-30b, and 

the vertical shear ∂U / ∂z in Figure 9-30c. In the STC03 stability class we see that the jets  D 

within the turbine layer (below 120 m) occur in less stable environments with smaller shear 

stresses and vertical shears across the turbine rotors. Figure 9-31a, a characteristic jet profile 

plots the smoothed profiles of the variation of the median jet maximum velocities and 

accompanying wind directions. Figure 9-31b shows the corresponding variations in the RiTL and 

273
 
 

 

9 

Figure 9-29. Probability distributions of Lamar site LLJ characteristics with height: (a) time period; 

(b) wind direction at LLJ maximum; and (c) wind speed of LLJ maximum for the STC02, STC03, 

STC04, and STC05 stability classes. The largest turbine dynamic responses occur in the STC03 

class. The boxplot dots represent the P05 and P95 percentiles. 

274 
 

Figure 9-30. Probability distributions by stability class of WindPACT (GE) 1.5-MW rotor layer 

turbulence scaling parameters for corresponding LLJ heights: (a) z/LD; (b) u*D; and (c) U / z .  D 

275 
31
 

Figure 9-31. . Vertical profiles of the median: (a) LLJ peak UH and corresponding wind direction 

WD; (b) RiTL and rotor disk layer mean z/L; (c) rotor disk layer mean u* and U / z

 for subset of 

sodar vertical profiles that reached 500 m. 

disk rotor layer mean M-O z/LD stability parameters. These curves indicate that the stronger jets 

at higher altitudes contribute to destabilizing the rotor disk layer while increasing the shearing 

stress u*D (downward momentum flux) and vertical shear across it, as shown in Figure 9-31c. 

Our MLR analysis found that shape and magnitude of the jet profiles associated with a given jet 

maximum height scaled with the jet maximum velocity, RiTL, and u*D. The modeled mean jet 

velocity profile is then expressed as 

10 

Uz z () cn Tn () (9-13) U n0 

and the corresponding mean wind direction profile is 

276 
 

 

 

 

 

 

 

 

 

 

10 

Φ() z = ∑cT () (9-14) n n z , Φ

n=0 

where cnU and cn are the Chebyshev coefficients for the velocity and wind direction and Tn are Φ

the corresponding n

th order Chebyshev polynomials. The modeled jet speed and direction 

profiles given by Equations 9-13 and 9-14 are thus scaled by 

cn = c1, n U jet + c2,n Ri TL + c3, n u*D + c4,n (9-15) U U max U U U

and 

c . (9-16) n = c1, n U jet + c2,n Ri TL + c3, n u*D + c max 4,n Φ Φ Φ Φ Φ

The height of the jet Zjet and its U jet are specified by the user or random defaults can be used. max 

Figure 9-32 plots the observed U jet velocities with height. max 

Figures 9-33, 9-34, and 9-35 show the sensitivity of the shape of the vertical profiles of wind 

speed, wind direction, and wind speed standard deviation to variations in U jet , RiTL, and u*D max 

and the influence on the wind speed, direction, and turbulence level (σU) profiles. In Figure 9-33 

we vary U jet over ranges characteristic of the 80-, 260-, and 460-m jet heights for RiTL of +0.50 max 

and +0.05. The most noticeable variation is in the wind direction profile associated with an 80-m 

jet height. The results in the variations of RiTL in Figure 5-34 are most pronounced in both the 

wind speed and direction profiles for a 460-m jet height. Finally, the results of varying the mean 

turbine layer shearing stress in Figure 9-35 are most pronounced in the wind direction profiles 

for a 460-m jet height though some smaller effects are seen in both the wind speed and direction 

for jet heights of 80 and 260 m. Figure 9-36 illustrates examples of 80-, 260-, and 400-m lowlevel jet wind speed and direction profiles generated by the TurbSim GP_LLJ spectral model for 

an 80-m mean wind speed of 12 m s–1 and an RiTL of +0.05. The significant speed shears over 

deep vertical layers for the 260- and 400-m heights are quite evident and are potential source 

regions for KHI and downward fluxes of Ecoh. 

277
 
Figure 9-32. Observed Lamar site maximum LLJ velocities with height 

278 
Figure 9-33. GP_LLJ model profile variations for 80-, 260-, and 460-m jet heights with variations in
 

Ujet and RiTL values of +0.50 and +0.05. The three lower dashed lines represent the rotor disk max 

layer and hub height of the WindPACT 1.5-MW turbine and the upper is an approximate maximum 

elevation of a 10-MW turbine rotor. 

279 
Figure 9-34. GP_LLJ model profile variations for 80-, 260-, and 460-m jet heights with variations in
 

RiTL and u*D values of +0.2 and +0.6 m s–1
 

280 
 

Figure 9-35. GP_LLJ model profile variations for 80-, 260-, and 460-m jet heights with variations in 

u*D and RiTL values of +0.50 and +0.05 

281 
 

 

Figure 9-36. Examples of three TurbSim GP_LLJ spectral model LLJ wind speed and direction 

profiles for 80-m mean wind speed of 12 m s–1 and RiTL of +0.05. The wind direction is relative to 

the direction at 80 m. 

282 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9.4.7 TurbSim Spatial Simulations

An example of the spatial aspects of the TurbSim simulated turbulent inflow NWTCUP spectral 

model is scaled based on measurements from the ART upwind planar array at 0730 MST on 

December 15, 2001. The specified boundary conditions derived from the measurements and 

required for this simulation are shown above the dashed line in the following list and other nonscaling but supplementary measured results are below it: 

• Hub-height mean wind speed of 12.78 m s–1 

• RiTL of +0.020 

• Disk-averaged mean shearing stress u*D of 0.711 m s–1 

• Disk layer power law exponent α of 0.103
 

• ---------------------------------------------------------------------­

• Hub peak value of Ecoh of 15.2 m2 s

–2 

• Disk-diameter normalized buoyancy length scale Lb/D of 1.27. 

The parameters below the dashed line are not used as boundary conditions but are given for 

reference. Figure 9-37 plots isocontours of Ecoh from a single simulation realization for 290 to 

330 seconds of the 600-second simulated record. No coherent structures were added to the 

simulated background flow in Figure 9-37a but were added in Figure 9-37b. An examination of 

the latter reveals the presence of larger areas of 7.5 or greater values (red and black) of Ecoh than 

in the former. 

The most turbulent episode recorded by the LIST experiment occurred late in the 10-minute 

record on February 5, 2001, at 0505 MST. We simulated the near-rated wind speed turbulent 

inflow with the TurbSim NWTCUP spectral model using the following 10-minute mean values 

measured on the upwind planar array: 

• Hub-height mean wind speed of 12.58 m s–1 

• RiTL of +0.017 

• Disk-averaged mean shearing stress u*D of 0.702 m s–1 

• Disk-layer power law exponent α of 0.108
 

• -----------------------------------------------------------------­

• Hub peak value Ecoh of 80 m2 s

–2 

• Disk-diameter normalized buoyancy length scale Lb/D of 3.01. 

283
 
 

Figure 9-37. TurbSim simulation of NWTC LIST ART inflow observation of December 15, 2001, at 

0736 MST. Isocontours of simulated Ecoh (a) without coherent structures and (b) with coherent 

structures. 

284 
 

 

 

 

 

 

Figure 9-38 plots isocontours of the u, v, and w turbulence components and Ecoh from a single 

TurbSim stochastic simulation realization for 550 to 600 seconds. The complex, 3-D turbulent 

structure is very evident. Values of Ecoh reach more than 30 m2 

s

–2 during the very intense and 

coherent turbulent period from about 580 to 588 seconds. Figure 9-38a does not include any 

superimposed coherent structures, but Figure 9-38b does. As with Figure 9-37, adding these 

structures increased the size and intensity of the coherent turbulent patches in the simulated 

background flow. 

In Figure 9-39 we plot the isocontours of Ecoh from a TurbSim GP_LLJ spectral model 

simulation of a much less turbulent situation. Here we simulate a typical Great Plains inflow to 

the NREL 5-MW Reference Turbine without the presence of a low-level jet and accompanying 

coherent structures. The mean hub-height wind speed is above rated wind speed at 13 m s

–1, the 

RiTL is +0.02, the disk-layer u*D is 0.422 m s–1, and the rotor disk shear exponent α is 0.139. 

Default values were used for the remaining boundary conditions. At the beginning of the 

simulated record in Figure 9-39a there is a small coherent structure with a small and more 

intense core that dies away rather quickly. For the period of 125 to 225 seconds in Figure 9-39b, 

larger patches of Ecoh reappear but their intensity is at the turbine dynamic response threshold of 

2 m2 

s

–2 and most likely a low level of vibratory excitation is developing in the structure. 

285
 
(a) 

Figure 9-38. TurbSim simulation of intense LIST ART inflow turbulence observation, February 5, 2001, 0505 MST: 

structures and (b) with coherent structures 

286 
Figure 9-39. TurbSim GP_LLJ spectral model simulation of inflow Ecoh to NREL 5-MW Reference 

turbine without LLJ and no coherent structures: (a) –5 to +50 seconds and (b) 125- to 225-second 

periods 

287 
 

 

 

 

 

 

 

 

 

 

9.5 Validation of TurbSim NWTCUP and GP_LLJ Spectral Models

We validated the TurbSim wind farm (WF_UPW, WF_07D, and, WF_14D), NWTCUP, and 

GP_LLJ site-specific spectral models. This was accomplished obtaining the median values of a 

range of turbulence parameters from the P05–P95 distributions from the observations taken in 

the wind farm, the NWTC upwind planar array, and the Lamar site 120-m met tower. We used 2 

m s

–1 wind speed bins over a range of 2 to 24 m s–1and the previously defined stability classes 

(STC01, STC02, STC03, STC04, and STC05) to make the problem more tractable. Table 9-7 

summarizes these wind speed bins. We applied the bin medians as the TurbSim boundary 

conditions to calculate an ensemble of 31 stochastic realizations for each site. In Figure 9-40 we 

present boxplot distributions from the NWTC and the Lamar site of the P05–P95 measured 

subpopulations and the aggregate distributions from the 31 simulation ensemble for the hubheight local u* and peak or maximum value of Ecoh. The distributions of observed u* in Figure 9­

40 reflect the variation in the actual flow, and the simulated results reflect the observed 

population median that was used for scaling. There is, however, no such constraint on the peak 

values of Ecoh. In general, the simulated distributions of this important parameter track the 

observed ones very well. 

In Figure 9-41 we compare the distributions of the measured hub-height turbulent component 

standard deviations σ σ, , and σ for the NWTC and Lamar sites with the aggregate u v w 

distributions of the simulated ensembles. Our goal was to have the Q1–Q3 IQR (P25–P75) of 

simulated results to fall within at least the P10–P90 range of the observations. An examination of 

Figures 9-41a and b shows that in general simulated distributions fall close to the observed Q1– 

Q3 quartile range, but the NWTC σu and σw have a tendency to be negatively biased. Figure 9-42 

compares distributions of the observed hub-height mean Reynolds stress components and the 

simulated ones. Again, because of the relationship between u* and uw ' ' there is no variation in 

the former because it was a specified scaling parameter. There are generally reasonable 

agreements with the u v' and ' vw ' ' components, though the NWTCUP model predicted values 

exhibit much wider distributions than those seen with the GP_LLJ model. 

Table 9-7. Wind Speed Bin Classification 

Bin Value 

Speed 

Range 

(m s

–1) 

3 2–4 

5 4–6 

7 6–8 

9 8–10 

11 10–12 

13 12–14 

15 14–16 

17 16–18 

19 18–20 

21 20–22 

23 22–24 

288
 
Figure 9-40. Statistical comparisons of observed probability distributions of P05–P95 range 

observed hub-height u* and peak Ecoh with stability and mean wind speed classes with NWTCUP 

and GP_LLJ TurbSim simulations using observed median values for boundary conditions: (a) 

NWTCUP and (b) GP_LLJ 

289 
Figure 9-41. Same as Figure 9-40, but observed hub-height σu, σv, and σw with NWTCUP and 

GP_LLJ TurbSim simulations using observed median values for boundary conditions: (a) 

NWTCUP and (b) GP_LLJ
 

290 
Figure 9-42. Same as Figure 9-40, but for observed hub-height mean u'w', u'v', and v'w' Reynolds 

stresses with NWTCUP and GP_LLJ TurbSim simulations using observed median values for nine 

boundary conditions: (a) NWTCUP and (b) GP_LLJ 

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10.0 Summary and Conclusions 

Using simultaneous, time-synchronized measurements of the turbulent inflow microscale 

characteristics and the dynamic response of wind turbine structural components, we developed 

an understanding of the role of the physics of the inflow turbulence characteristics in creating 

excessive loads and fatigue damage in turbine structures. We used data collected from two 

adjacent 65-kW turbines deep within a 41-row wind farm in San Gorgonio, California; a 600-kW 

turbine operated in the rigorous flow at the National Wind Technology Center (NWTC) near 

Boulder, Colorado; and in atmospheric conditions at the site of a since installed wind farm on the 

high plains of southeastern Colorado. Analyzing these data allowed us to identify a narrow range 

of critical atmospheric conditions common to the sites. These atmospheric conditions are 

responsible for the majority if not all of the turbulence-induced fatigue damage seen on the two 

turbines in California and at the NWTC. 

In this report we discussed the evolution of our understanding of the impact of atmospheric 

turbulence on wind turbines, along with the atmospheric conditions that create the specific 

turbulence characteristics that are so damaging. We also described how we developed a 

computer code that simulates these characteristics for use with the turbine models and design 

codes. We now summarize our conclusions in each of these areas. 

10.1 The Impact of Turbulence on Turbine Dynamics

Our measurements and analysis enabled us to identify the role that organized or coherent 

turbulent patches in the background flow play in inducing large load excursions and fatigue 

damage. Using both numerical simulations and physical measurements, we showed that a 

resonant coupling of kinetic energy exists between these coherent turbulent patches and the 

natural vibrational modes of the turbine blades as the turbulence passes through the rotor. These 

organized turbulent patches frequently develop within the much more random turbulent and 

vertically sheared background flow of the stable, nocturnal boundary layer because of 

atmospheric Kelvin-Helmholtz Instability (KHI). KHI is a form of atmospheric resonance 

brought about by the influence of buoyancy on the intensification of turbulent perturbations 

moving through the background or mean flow. The fluctuating velocities of these resonant flows 

are spatially and temporally organized and can create a similar response characteristic induced 

by the unsteady aerodynamics of a turbine blade (i.e., the additive superposition of modal 

excursions into a large, phase-coherent load excursion). This process induces a flux or transport 

of turbulent energy into the blade structure, which is then propagated through the root 

attachments, the drivetrain, and the remainder of the structure. 

Simply put, a coherent turbulent structure ingested by a turbine rotor blade induces a coherent 

aeroelastic response in the turbine structure. The turbine’s design and the dynamic characteristics 

of its load paths—their modal frequencies and damping—determines how this energy is 

propagated through the turbine structure and where it is ultimately dissipated. As towers 

continued to be built taller, and turbine rotors become much larger and more flexible, the role of 

this process has likely become more influential in creating fatigue damage throughout the turbine 

structure. 

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10.2 Atmospheric Dynamics Associated with Turbine Dynamic Response

We showed that coherent turbulent kinetic energy—both locally generated and transported—is a 

major contributor to increased turbine fatigue damage. Kelvin-Helmholtz Instability (KHI) is 

often the most dominant process that creates these important turbine inflow turbulence 

characteristics. KHI is associated with stable, sheared flows that are the hallmark of the nocturnal 

atmospheric boundary layer. Often, the depth of the atmospheric boundary layer within which 

turbines reside exhibits stable characteristics approaching two-thirds of a diurnal period. 

We found that the vertical dynamic stability of the atmospheric layer inhabited by a turbine is 

one of the most influential atmospheric parameters affecting loading and fatigue damage. More 

specifically, we discovered a very narrow range of weakly stable conditions that is most 

damaging to turbine structures. It is within this critical stability range that the development of 

KHI and the attendant coherent turbulence occurs. Such damaging conditions are more likely to 

occur within certain periods of the stable portion of a normal diurnal cycle (i.e., typically during 

the early evening hours after sunset and again in the early morning hours between midnight and 

sunrise). During both of these periods, significant vertical shears can develop from the rapid 

changes that take place at sunset when convective turbulence ceases, as well as later, when 

atmospheric inertial oscillations contribute to the maximum strength of low-level jet streams 

(LLJs). In both cases conditions are ripe for the development of KHI. 

KHI creates organized or coherent turbulent perturbations, which propagate through the mean 

flow when the turbine layer stability falls within the critical range, that grow and intensify 

rapidly. We found that the greatest turbine dynamic response takes place when the fastest 

growing turbulent eddy size is near the equivalent diameter dimension of the turbine rotor. We 

also found that the vertical transport or flux of coherent turbulence into a turbine rotor disk layer 

is an important source of turbine dynamic response. This was true within the California wind 

farm and at the NWTC. Strong vertical fluxes exist in both locations, caused in California by the 

presence of the large wind farm itself combined with nearby mountainous terrain, and at the 

NWTC by the adjacent mountainous landscape. Our purpose in making turbulence 

measurements associated with an LLJ was to identify the presence, intensity, and frequency of 

the coherent turbulence conditions we found using the 65- and 600-kW turbines. The Great 

Plains hold the greatest wind resource in the United States, but they are also known to harbor 

strong, nocturnal LLJs and intense vertical shears beneath the jet maximum velocities. By 

combining direct measurements from a 120-m met tower and remotely sensed velocity 

measurements using an acoustic wind profiler (sodar)—and, for a short period, a scanning 

lidar—we found that such conditions do indeed exist, though often with less intensity than are 

observed in the California wind farm and at the NWTC. The diurnal occurrence was similar to 

what we found in the wind farm and at the NWTC, indicating that the responsible nocturnal 

boundary layer dynamics that are responsible for the observed excessive turbine dynamic 

responses are more ubiquitous and extend to a much greater range of wind energy sites. We also 

found that the presence of LLJs well above the maximum height of turbine rotors was often 

responsible for significant downward fluxes of coherent turbulent energy similar to those seen in 

lee flows downwind of mountainous terrain. These LLJs, then, are an important source of this 

turbine-sensitive turbulence characteristic. 

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10.3 Simulating Critical Turbulence Characteristics

The TurbSim stochastic inflow turbulence code was developed to produce numerical simulations 

of full-field flows that mimic the statistical characteristics of inflow turbulence over a wide range 

of turbine operating conditions. We extended Paul Veers’ (Sandia National Laboratories) 

original SNLWIND simulator to include all three turbulent wind components in a diabatic as 

well as neutrally stable atmosphere. We used field measurements from the California wind farm 

and an upwind planar array at the NWTC, as well as from a 120-m met tower and acoustic wind 

profiler at the Lamar site, to develop individual site-specific spectral models to simulate the 

conditions in each location. Once we identified KHI as major contributor to the largest turbine 

dynamic loads, colleagues at the National Center for Atmospheric Research created a highresolution simulation of the life cycle of a stationary Kelvin-Helmholtz (K-H) billow turbulent 

structure. 

We incorporated several well-defined excerpts from this simulation in the TurbSim code along 

with similar ones derived from an even more highly resolved K-H billow simulation furnished by 

our colleagues at Colorado Research Associates. Adding the coherent structure elements derived 

from the high-resolution K-H billow simulations (and scaled based on actual measurements) 

allowed us to correct the under prediction of fatigue damage caused by a TurbSim predecessor. 

Including wind direction profiles in addition to velocity in the simulation of LLJs also revealed 

an important source of dynamic loads associated with wind direction shear across the rotor disk. 

Statistical summaries of the TurbSim simulations compared well with observed summaries, 

particularly for the NWTC and Great Plains spectral models where larger data sets were 

available for analysis. Limited validations of the observed and simulated loads for the 600-kW 

turbine in the NWTC operating environment showed them to be in reasonable agreement. 

Similar validations for the wind farm and Great Plains spectral models have been hampered by 

the lack of a more complete dynamics model of the 65-kW turbines at the wind farm and by only 

virtual models of the simulated 1.5- and 5-MW turbines being available. 

We believe the TurbSim site-specific spectral models give the turbine designer a range of 

realistic emulations of the full-field turbulent inflows seen in each environment, particularly 

within the critical stability range. Such conditions are not available in the current International 

Electrotechnical Commission (IEC) Normal Turbulence Models (NTMs). We highly recommend 

that designers use the TurbSim NWTC and Great Plains spectral models, particularly with added 

emphasis on the critical range stability boundary conditions to bracket a range of likely wind 

turbine operating conditions. Finally, we also encourage designers to employ one of the available 

multibody turbine dynamic codes that use the NREL AeroDyn code as the interface with 

TurbSim for such simulations. 

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