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Contract No. DE-AC36-08GO28308

The Effects of Second-Order 

Hydrodynamics on a 

Semisubmersible Floating 

Offshore Wind Turbine

Preprint

I. Bayati

Politecnico di Milano

J. Jonkman, A. Robertson, and A. Platt

National Renewable Energy Laboratory

Presented at the Science of Making Torque from Wind

Technical University of Denmark, Copenhagen

June 17–20, 2014

Conference Paper

NREL/CP-5000-61752

July 2014
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The effects of second-order hydrodynamics on a 

semisubmersible floating offshore wind turbine

I Bayati1, J Jonkman2, A Robertson2 and A Platt2

1 Politecnico di Milano, Dipartimento di Meccanica, Milano, Italy 2 National Renewable Energy Laboratory (NREL), Golden, CO, USA

E-mail: ilmasandrea.bayati@polimi.it, jason.jonkman@nrel.gov, amy.robertson@nrel.gov, 

andrew.platt@nrel.gov

Abstract. The objective of this paper is to assess the second-order hydrodynamic effects on a 

semisubmersible floating offshore wind turbine. Second-order hydrodynamics induce loads and 

motions at the sum- and difference-frequencies of the incident waves. These effects have often been 

ignored in offshore wind analysis, under the assumption that they are significantly smaller than firstorder effects. The sum- and difference-frequency loads can, however, excite eigenfrequencies of a 

floating system, leading to large oscillations that strain the mooring system or vibrations that cause 

fatigue damage to the structure. Observations of supposed second-order responses in wave-tank tests 

performed by the DeepCwind consortium at the Maritime Research Institute Netherlands (MARIN) 

offshore basin suggest that these effects might be more important than originally expected. These 

observations inspired interest in investigating how second-order excitation affects floating offshore 

wind turbines and whether second-order hydrodynamics should be included in offshore wind 

simulation tools like FAST. In this work, the effects of second-order hydrodynamics on a floating 

semisubmersible offshore wind turbine are investigated. Because FAST is currently unable to account 

for second-order effects, a method to assess these effects was applied in which linearized properties of 

the floating wind system derived from FAST (including the 6x6 mass and stiffness matrices) are used 

by WAMIT to solve the first- and second-order hydrodynamics problems in the frequency domain. 

The method was applied to the Offshore Code Comparison Collaboration Continuation (OC4)-

DeepCwind semisubmersible platform, supporting the National Renewable Energy Laboratory’s 5-

MW baseline wind turbine. In this paper, the loads and response of the system caused by the secondorder hydrodynamics are analyzed and compared to the first-order hydrodynamic loads and induced 

motions in the frequency domain. Further, the second-order loads and induced response data are 

compared to the loads and motions induced by aerodynamic loading as solved by FAST.

1. Introduction

Nowadays offshore wind energy is moving to deeper waters, where floating platforms seem to be the most 

suitable solution. This paper aims to assess the effects of second-order hydrodynamics on the overall dynamics of a 

semisubmersible platform combined with the National Renewable Energy Laboratory’s (NREL’s) 5-MW reference 

wind turbine [1]. 

Presently, most aero-hydro-servo-elastic simulation tools used for designing floating offshore wind turbines

include only first-order hydrodynamics, which induce loads and motions that vary with the same frequency as the 

incident waves; however, the offshore oil and gas industry has demonstrated the importance of second-order 

hydrodynamics—solved either directly or with Newman’s approximation [2] on floating system design. Secondorder hydrodynamics can induce loads at the sum- and difference-frequencies of the incident wave components, 

which can excite eigenfrequencies of the system, leading to large oscillations that strain the mooring system or 
2 

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vibrations that cause fatigue damage to the structure. A recent study assessed the importance of second-order 

hydrodynamics on the Offshore Code Comparison Collaboration (OC3)-Hywind spar buoy and University of Maine

tension-leg platform (TLP) floating offshore wind turbine (FOWT) concepts [3]. In this paper, the approach defined 

in [3] was applied to analyze the semisubmersible platform designed by the University of Maine and used within the 

International Energy Agency (IEA) Wind Task 30 Offshore Code Comparison Collaboration Continuation (OC4) 

project, shown in figure 1 [4]. A 1/50th Froude-scaled model of this system was tested in a wind/wave basin at the 

Maritime Research Institute Netherlands (MARIN) in 2011 [5] by the DeepCwind consortium. Validation of a 

FAST model using this test data showed evidence of the importance of considering second-order hydrodynamics; 

particularly, second-order difference-frequency wave-diffraction loading played a significant role in the global 

response of the floating semisubmersible system because the surge, pitch, and heave natural frequencies are lower

than the wave-frequency band. The low-frequency wind energy from atmospheric turbulence also excites the wind 

turbine in the same frequency band. The wind forcing and first-order hydrodynamic loading is captured by FAST, 

but neglecting the second-order hydrodynamics inevitably underestimates the global response.

2. Second-order hydrodynamics

Potential flow theory considers the flow around a body to be incompressible, inviscid, and irrotational, with 

negligible surface-tension effects. The kinematics of the problem is typically described by a global coordinate 

system (GCS) that is located in an inertial frame of reference and assumed to be a right-handed Cartesian system 

with its origin located at the still water level. A second body-fixed coordinate system (BCS) that moves with the 

body has its axis coincident with the GCS when the body is in an undisturbed (mean) position. First-order theory for 

potential flow assumes a linear free-surface boundary condition and ignores nonlinear wave-body interaction effects.

The first-order velocity potential is solved about the mean position of the body and the total hydrodynamic problem 

is solved by means of superposition of the independent solutions of subproblems, such that the radiation (i.e., the 

problem of the interactions caused by forced motions of the body in calm water), diffraction (i.e., the problem of the 

interactions of the incident waves with the body held fixed), and hydrostatic problems (i.e., the problem of buoyancy 

change with body displacement) can be solved independently. This superposition approach is valid mainly for a 

floating system with small translational displacements compared to the wave length and small rotations with respect 

to the wave steepness. Second-order hydrodynamic theory more accurately approximates the nonlinear free-surface 

boundary condition and wave-body interactions, including the quadratic interaction of first-order quantities. These 

hydrodynamics are computed by means of the superposition of the quadratic interaction of terms related to the firstorder velocity potential, as well as terms given by the solution of the second-order velocity potential. The latter is 

derived by second-order Taylor expansion of the velocity potential, along with the expansion of the motion 

amplitude and wave elevation. Therefore, the velocity potential boundary value problem of the moving body is 

reformulated and solved with respect to a GCS. 

The hydrodynamic forces and moments that result from the interaction of the fluid with a floating structure are 

obtained through the integration of the fluid pressure over the instantaneous wetted surface of the structure. Both 

first- and second-order approaches approximate this computation over the mean wetted profile of the floating 

structure; however, the assumption of inviscid flow limits the amount of hydrodynamic damping considered, 

requiring the potential-flow solution to be augmented with viscous effects where important. This augmentation is 

typically done by increasing the potential-flow solution with the viscous drag term from Morison’s equation in a 

time-domain analysis to perform a more realistic simulation of the actual dynamics of such systems, as discussed in 

[6], [7]. 

Second-order hydrodynamic loads are proportional to the square of the wave amplitude and have frequencies that 

are equal to both the sum and the difference of pairs of incident wave frequencies. This means that, although the 

natural frequencies of the structure are designed to be outside the first-order wave-energy spectrum, the secondorder loads can excite these frequencies. Therefore, despite the second-order hydrodynamic loads normally being 

small in magnitude, the resonant effect can be significant. 

Three components of second-order hydrodynamic loads can be defined: the mean-drift loads, the differencefrequency/slow-varying drift loads, and the sum-frequency loads. The mean-drift loads result in a mean offset of the 

body relative to its undisplaced position. The slow-varying loads are the result of quadratic interactions between 

separate wave components in an irregular sea state that have different frequencies. These loads can excite large 

amplitude resonant motion of the floating platform at low frequency. The sum-frequency loads have a frequency that 

is higher than the wave frequency and are also generally small in amplitude. They arise from the same source as 

low-frequency drift forces, that is, from quadratic interactions between separate wave components in an irregular sea 

state. The contribution from these loads can be particularly important in relation to a “springing” and “ringing” 

phenomenon for floating wind turbine configurations with taut moorings, such as TLP concepts that typically have 
3 

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high natural frequencies in heave, roll, and pitch. The sum-frequency second-order loads can also potentially excite 

vibration modes of the wind turbine [8]. 

The focus of this paper is to investigate the influence of second-order hydrodynamics on the OC4-DeepCwind 

floating semisubmersible system. Model validation work previously performed with this system using the MARIN 

tank data adopted Newman’s slow-varying load approximation [5]. According to this approximation [2], the offdiagonal components of the difference-frequency quadratic transfer functions (QTFs) can be approximated by 

manipulating the diagonal values. Newman’s approximation is valid when the natural frequencies of slowly varying 

motions are small, as in the present case. Nevertheless, this approximation may not be very reliable in shallow 

water, broad-banded sea states, or sea states with wave direction spreading. In the validation work of [5], a custom 

FAST tool was implemented using the second-order wave diffraction forces from Newman’s approximation 

associated with the surge degree of freedom (DOF). In this paper, however, the unapproximated second-order loads

were computed by WAMIT for all six DOFs [9]. 

3. Simulation tools and approach

To investigate the impact of second-order effects on the OC4-DeepCwind floating semisubmersible system, a 

combined modeling approach that incorporates WAMIT and FAST was used. In this section, the method will be 

explained, as it differs from the direct use of FAST in its present form. The two simulation tools used to assess the 

second-order effects in this work are FAST and WAMIT. FAST is a publicly available wind turbine simulation tool 

developed by NREL [6], [10] that predicts the coupled dynamic response of the entire FOWT in the time domain, 

thereby taking aerodynamics, structural elasticity, control logic, and first-order hydrodynamics plus viscous effects

into account. WAMIT is a commercial, three-dimensional panel code designed to compute the hydrodynamic 

loading and response of floating bodies in the frequency domain [9], including first-order wave-exciting loads and 

response amplitude operators (RAOs), as well as the second-order load and response QTFs. WAMIT is widely used 

in the offshore industry and is capable of solving both the first- and second-order hydrodynamic problems for a rigid 

structure of arbitrary geometry. Currently, the coupled response of FOWTs simulated in FAST considers only firstorder hydrodynamic quantities computed by WAMIT or an equivalent pre-processor. As a result, the procedure

employed in this work to assess second-order hydrodynamics effects uses the approach developed in [3] that is

briefly summarized below (shown in figure 2). 

Figure 1. OC4-DeepCwind 

semisubmersible.

Figure 2. Procedure to assess first- and second-order hydrodynamics of the 

OC4 semisubmersible FOWT.

First, WAMIT was used to calculate the hydrostatic restoring (Chydro), frequency-dependent hydrodynamic added 

mass and damping matrices from wave radiation (A(f) and B(f)), and the frequency- and direction-dependent 

hydrodynamic force coefficients from wave diffraction (X(f)). These quantities are WAMIT outputs, based on the 

geometry of the submerged portion of the floating platform. It must also be stated that the investigation of the effect 

of a multidirectional sea state is beyond the aim of this work, therefore only one heading angle β=0 on which the 

velocity potential is dependent was considered in the computations reported in this paper. In addition, the wind was 

aligned with the waves with no yaw misalignment. Second, the hydrodynamic quantities were given as inputs to 

FAST, together with inputs related to the wind turbine, floating platform, and mooring system specifications. The 
4 

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FAST model was then used to compute the 6x6 mass matrix of the entire wind system (Mlin) and the 6x6 stiffness 

matrix of the mooring system (Clin) through a linearization procedure. Being careful to avoid double-booking terms, 

these quantities were imported back into WAMIT as external matrices for the third step—calculating the first- and 

second-order frequency-dependent loads and responses (RAOs and QTFs), considering the properties of the entire 

system. 

The natural frequencies of the OC4-DeepCwind semisubmersible platform were designed to fall below the wavefrequency range. Although viscous drag will tend to dominate the potential damping at these low frequencies, the 

first- and second-order WAMIT solutions were not augmented with linearized viscous effects. Nevertheless, as 

reported in [4] and [5], linear and quadratic damping is included in FAST for performing more realistic time-domain 

simulations. An important limitation to the calculation in WAMIT is that the structure is modelled as a rigid body, 

whereas FAST can model the structural elasticity. It should also be noted that wind turbine operational effects, such 

as rotor gyroscopics, aerodynamic damping, and aerodynamic stiffness, were ignored in the linearized matrices 

imported to WAMIT. 

FAST is currently not configured to utilize the second-order force QTFs calculated by WAMIT. Therefore, the 

assessment summarized in this paper was conducted outside of FAST and within WAMIT only, by using FAST 

merely for generating the linearized matrices mentioned above and to perform simulations to compute the global 

response caused by the wind-wave and wave-only first-order hydrodynamic loads. The comparison between 

WAMIT and FAST was then possible by converting FAST’s time-domain outputs to the frequency domain. 

Regarding the WAMIT computations, the platform of figure 1 was discretized by a means of 1167 panels and a 

range of 56 wave frequencies in the interval [0.25 3.0] rad/s, with a frequency step of 0.05 rad/s using a high-order 

panel method. In the high-order computational approach, the potential on the body surface is represented by Bsplines in both the first- and second-order analyses. In the first-order analysis, the forcing on the body surface is 

assumed continuous and the integration is carried out by Gauss quadrature. In the second-order analysis, however, 

the integration of the quadratic forcing on the body and the free surface is performed piecewise in the same manner 

as for the low-order analysis. 

4. Post processing and results

In this section, the hydrodynamic loads and response of the floating semisubmersible (using the approach 

described above) are analyzed by considering the following DOFs: surge, pitch, and heave. These DOFs have 

associated natural frequencies of 0.01 Hz, 0.04 Hz, and 0.055 Hz, respectively. Figures 3, 4, and 5 show the firstorder hydrodynamics solutions in terms of wave exciting loads X(f) = |X(f)|eiφx and motion response amplitude 

operators RAO(f) = |RAO(f)|eiφRAO, whose magnitudes are provided by WAMIT as normalized per unit wave 

height, for a water depth of 200 m. The variation of load magnitude across the frequencies is a result of the 

interaction of the waves with the three distinct columns of the OC4-DeepCwind floating semisubmersible system; 

the natural frequencies are clearly visible in the RAOs. The very high magnitude corresponding to these frequencies 

is consistent with the lack of a significant damping in the model.

Similar to the first-order analysis, the second-order WAMIT outputs are normalized by pairs of incident wave 

amplitudes, so that it is possible to define the complex second-order loads Fjk

± = �Fjk±� eiφjk±

and responses 

ξjk

± = �ξjk±� eiφjk±

, where �Fjk

±� and �ξjk

±� are the load and motion QTF magnitudes per square unit wave 

amplitude with phase φjk± that are associated with the complex wave-amplitude pairs, Aj

± = �Aj� eiφj and Ak± =

|Ak| eiφk, at frequencies fj and fk, with the related random phases φj and φk, respectively. The magnitudes of the 

difference-frequency components of the second-order load and response QTFs are reported in figures 6, 7, and 8. In 

the left figures, the symmetry is clearly visible with respect to the anti-diagonal, which is related to the mean-drift 

load that occurs at f− = fj − fk = 0 resulting in a static load. With regards to figures 6, 7, and 8 (left), lines parallel to 

the anti-diagonals (solid black line) pertain to a given difference frequency f−, whereas lines parallel to the main 

diagonals (dashed black lines) pertain to a given sum-frequency. Figures 6 and 7 show that, mainly for surge but 

also for pitch, the second-order wave-exciting loads are large in magnitude over a wide interval of difference 

frequencies, suggesting that the approximation of the second-order loads by a means of only a few off-diagonals 

would result in an underestimation of the overall loading for this platform. Figures 6, 7, and 8 also report (right) the 

difference-frequency QTF responses as a function of difference frequency. The choice of a different plotting format, 

with respect to the correspondent QTF loads (left), is because there are noticeable magnitudes in the response at 

specific frequencies (i.e., the natural frequencies, that lie near the anti-diagonals). The clearly visible peaks in 

figures 6, 7, and 8 are related to (respectively) the surge, pitch, and heave natural frequencies. The surge and pitch 

natural frequencies are visible in both figures 6 and 7 because the two DOFs are coupled.
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Figure 3. Surge first-order solution: wave-exciting force (left) and response magnitude (right). 

Figure 4. Pitch first-order solution: wave-exciting moment (left) and response magnitude (right). 

Figure 5. Heave first-order solution: wave-exciting force (left) and response magnitude (right). 
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Figure 6. Difference-frequency surge: QTF force (left) and response magnitude (right). 

Figure 7. Difference-frequency pitch: QTF moment (left) and response (right) magnitude.

Figure 8. Difference-frequency heave QTF force (left) and response magnitude (right). 
7 

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Using these RAOs and QTFs, global responses and loads were calculated for a variety of sea states. For a given 

sea state, different time-domain realizations lead to different global responses and loads because of the different 

combination of individual wave phases [4]. The sea state considered for the simulations reported herein was the 

JONSWAP spectrum with a significant wave height Hs = 2 m and peak-spectral period Tp = 7.5 s and the results 

are shown in figures 9, 10, 11, and 12 (left). The choice of sea state was based on the desire to perform future 

comparisons between the numerical results and the experimental data from the tests performed at the MARIN 

wind/wave basin, as reported in [5]. In addition, a more severe sea state (Hs = 7 m and Tp = 10 s) was considered 

in figure 12 (right) to better demonstrate the importance of second-order hydrodynamics.

Figures 9, 10, and 11 were derived using equation (1), (2), (3), and (4). Equations (1) and (2) represent 

(respectively) the fast-Fourier transform (FFT) magnitudes of the first-order loads and response, whereas equations

(3) and (4) represent the second-order loads and response. The wave amplitudes are related to the wave spectrum by

the relation |A(f)| = �2S(f)df, where S(f) is the one-sided wave spectrum and has different random phases φa

at each frequency f. 

F(f) = �|X(f)||A(f)|ei(φx+φa)� = |X(f)||A(f)| (1)

ξ(f) = �|RAO(f)||A(f)|ei(φRAO+φa)� = |RAO(f)||A(f)| (2)

Ftot±�fl

±� = � � Fjk

±AjAk

fl=fj±fk

� = � � �Fjk

±��Aj�

fl=fj±fk

|Ak|ei(φjk±+φj+φk)

� (3)

Χtot±�fl

±� = � � ξjk±AjAk

fl=fj±fk

� = � � �ξjk

±��Aj�

fl=fj±fk

|Ak|ei(φjk±+φj+φk)

� (4)

In Figures 9, 10, and 11 the second-order results are reported both for loads and response and plotted along with 

the first-order results. What can be clearly seen from these graphs is: although the second-order loads are quite small 

compared to the first-order loads, particularly for the difference-frequency band, this loading results in nonnegligible responses with respect to first order. This results from the excitation of system natural frequencies and a 

small amount of damping. The very small amount of radiation damping at these frequencies results in large resonant 

motion. In reality, the response will be tempered by viscous damping and potentially aerodynamic damping when 

the turbine is operating. Although the sum-frequency contribution is not playing an important role for the OC4-

DeepCwind platform, the difference-frequency contribution is. In figures 9, 10, and 11, the results are processed by 

following the formulation of equations (3) and (4), and are analyzed for 15 different realizations for the given sea

state. Different realizations refer to variations in the random phase φjand φk for each realization. Also, the average 

loads and responses are reported along with the different realizations and the difference- and sum-frequency bands 

are shown in separate zoomed-in plots. The random phases do not impact the magnitude of the first-order loads and 

responses. 

In figure 12, the surge DOF was chosen to compare the power spectral densities (PSDs) computed in the 

frequency domain from WAMIT with the PSD of the time-domain response computed in FAST. A below-rated 

wind speed of 9 m/s was considered for the wind/wave simulation. As previously mentioned, low-frequency wind 

energy is responsible for exciting the surge natural frequency at 0.01 Hz, and also the pitch natural frequency at 0.04 

Hz. The PSD of the surge response was computed from FAST using the output time history, and the PSD from 

WAMIT was computed directly in the frequency domain using the second-order QTFs from WAMIT. The firstorder PSD was computed from the first-order RAO by the canonical form of equation (5), whereas the second-order 

PSDs were computed by the expressions proposed in [11], reported in equations (6) and (7): 

PSD(f) = |RAO(f)|

2S(f) (5)

Sξ

−(f−) = 8 � S(μ)S(μ + f−)|ξ−(μ, μ + f−)|

2dμ

∞

0

(6)

Sξ

+(f+) = 8 � S �

1

2

f+ + μ� S �

1

2

f+ − μ� �ξ+ �

1

2

f+ + μ,

1

2

f+ − μ��

2

dμ

1

2f+

0

(7)
8 

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where ξ−(f1, f2), and ξ+(f1, f2) of equations (6) and (7) refer to the difference- and sum-frequency motion QTFs 

at the frequencies f1 and f2. Regarding figure 12 (left), it can be noted that the FAST wave-only results match the 

WAMIT first-order results quite well and in this wave-frequency range the wave loads tend to dominate, whereas 

wind loads tend to dominate at low frequency over second-order difference-frequency loads. This observation was 

already noticed in the experimental scale tests at MARIN [5], which the present results agree quite well with. Also, 

in the case studied in Fig. 12 (left), the relationship between wind and wave environmental loads is considered to be 

representative of a realistic operating condition. Figure 12 (right) has a more severe sea state and the same 9-m/s 

wind speed of Fig. 12 (left), where a greater influence on the natural frequency excitation from the second-order 

difference-frequency loads is clearly visible. The difference-frequency hydrodynamic response now exceeds the

response from wind excitation.

For the floating semisubmersible type of platform, which is designed for having surge, heave, and pitch natural 

frequencies lower than the first-order wave spectrum frequency range, figure 12 suggests the need to calculate

difference-frequency loading in FAST along with the first-order loads to gather the realistic combined effect of lowfrequency wind and wave loading on the overall system dynamics, which is underestimated without considering 

second-order terms. The contribution of second-order sum-frequency loads are negligible for the OC4-DeepCwind 

platform; however, they are likely to be more important for a floating system such as a TLP [3]. 

Figure 9. Fast Fourier transform magnitude of the surge hydrodynamic force (left) and surge response (right). 

Sea state: JONSWAP spectrum with Hs = 2 m and Tp = 7.5 s. 

Figure 10. Fast Fourier transform magnitude of the pitch hydrodynamic moment (left) and pitch response 

(right). Sea state: JONSWAP spectrum with Hs = 2 m and Tp = 7.5 s. 
9 

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Figure 11. Fast Fourier transform magnitude of the heave hydrodynamic force (left) and heave response (right). Sea 

state: JONSWAP spectrum with Hs = 2 m and Tp = 7.5 s. 

Figure 12. Surge response power spectral density comparison between WAMIT and FAST. Wind speed: 9 m/s; Sea 

state: JONSWAP spectrum with Hs = 2 m and Tp = 7.5 s (left), Hs = 7 m and Tp = 10 s (right).

5. Conclusions

In this paper, an assessment of the second-order hydrodynamics on a semisubmersible floating offshore wind 

turbine is provided. The model analyzed in this work is the Offshore Code Collaboration Continuation-DeepCwind 

semisubmersible and the numerical tools considered are the aero-hydro-servo-elastic computer-aided-engineering

tool FAST for the turbine’s time-domain modeling and the panel code WAMIT for the frequency-domain 

hydrodynamics. FAST is currently capable of including only first-order hydrodynamics as computed by WAMIT, 

and so a novel approach was taken to analyze the effects of second-order hydrodynamics without complete coupling 

between the two tools . The wind turbine model was “included” in WAMIT by means of mass and stiffness matrices 

input as external matrices to WAMIT, derived from a FAST linearization procedure. Then the first- and secondorder hydrodynamics were computed in terms of difference- and sum-frequency load and response quadratic transfer 

functions (QTFs). A comparison between a first-order solution derived in FAST and the second-order solution from

WAMIT was then carried out. The results showed that difference-frequency second-order hydrodynamics are 

responsible for exciting the natural frequencies of the platform, which are designed to be lower than the first-order 

wave spectrum frequency range. The results also agreed with the experimental data gathered from the tests 

performed at the Maritime Research Institute Netherlands for the same platform concept. Although WAMIT likely

overestimates the response of the system because of the lack of viscous drag, it can be stated that, especially for 

severe sea states, the frequency content of second-order difference-frequency loads cannot be neglected in the 

dynamic analysis of such a system. 
10 

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Future work will involve modifying FAST to import and process second-order WAMIT-load QTFs for direct 

time-domain analysis of floating offshore wind turbines with second-order hydrodynamic effects [12].

6. Acknowledgments

The authors would like to acknowledge DeAnna Sewell from the University of Colorado-Boulder and Line 

Roald from ETH Zurich for their help in providing useful advice and results important to this work. This work was 

supported by the U.S. Department of Energy (DOE) under Contract No. DE-AC36-08GO28308 with the National 

Renewable Energy Laboratory. Funding for the work was provided by the DOE Office of Energy Efficiency and 

Renewable Energy, Wind and Water Power Technologies Office.

References

[1] Jonkman J, Butterfield S, Musial W and Scott G 2009 Definition of a 5-MW Reference Wind Turbine 

for Offshore System Development NREL/TP-500-38060 

[2] Newman J 1974 Second-order, Slowly-varying Forces on Vessels in Irregular Waves, In Proc Symp,

Dynamics of Marine Vehicles and Structures in Waves, pp. 182-6, Mechanical Engineering 

Publication Ltd, London

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