12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

LOW-ORDER REPRESENTATION OF THE WAKE DYNAMICS OF
OFFSHORE FLOATING WIND TURBINES

Cédric Raibaudo, Laurent Perret
LHEEA
Centrale Nantes
1 Rue de la Noë, 44300 Nantes, France
cedric.raibaudo@univ-orleans.fr

ABSTRACT

imental studies and full CFD. Low-order representation of thewake, less costly and capable of reproducing the full physicalphenomena, is therefore preferred. For this objective, modal
decomposition has been used to determine low-dimensionalmodel of the turbulent wind field (Bastine et al., 2018, 2015;
Hamilton et al., 2018; Sarmast et al., 2014; Saranyasoontorn& Manuel, 2005). Proper Orthogonal Decomposition (POD)is, in particular, a well-known method to extract the most energetic coherent structures in the flow (Sirovich, 1987). For
example, POD has been applied for wakes of an infinitely longrow of wind turbines (Andersen et al., 2014).
For floating wind turbines, modal decomposition was notmuch suggested yet. POD analysis was performed on generated wind fields using Mann and Kaimal turbulence models(Bachynski & Eliassen, 2019), or by associating LES simulations (Nybø et al., 2020). However, available synthetic turbulence models for generating these inflow conditions for simulations codes for performance and loads estimation are currently unable to account for all these interactions. Therefore,
being able to model the complex dynamics of the wind turbine
wake flow interacting with the atmospheric boundary layer toprovide unsteady aeroelastic computational codes with realistic inlet conditions is of crucial importance.
The objective of the present study is to show the potential and validity of a low-order representation of the flow obtained from synchronized hot-wire anemometry (HWA) andParticle Image Velocimetry (PIV) measurements performed in
the wind tunnel to accurately represent the wake flow dynamics. To this aim, realistic flow conditions are generated within
the wind tunnel, ensuring that the incoming boundary layer
and the wind turbine modeled by a porous disk are properly
scaled. In addition, the porous disk can also translate along
the longitudinal direction to mimic realistic surge-motion of afloating wind turbine. The velocity fields are reconstructed athigh temporal resolution using a dimensionality reduction andreconstruction approach based on both POD and multi-timedelay Stochastic Estimation, allowing for a detailed characterization of the dynamics of both the incoming boundary layer
and the wake flow developing downstream of the model.

A low-order representation of the wake downstream a
porous disk modeling a wind turbine is considered here. Synchronized Stereo-PIV measurements and hot-wire anemometry are performed to accurately represent the wake flow dynamics. Realistic flow conditions are generated, ensuring aproper scaling of the incoming boundary layer and the windturbine. The porous disk can also translate along the longitudinal direction to simulate realistic surge-motion of a floating
wind turbine. The velocity fields are reconstructed at higher
temporal resolution using POD and multi-time delay Linear
Stochastic Estimation, for the characterization of the full dynamics of both the boundary layer and the wake flow developing downstream of the model. The surge-motion imposedon the model shows to have a significant influence on the flow
dynamics, in particular on the temporal modes of the POD decomposition.

INTRODUCTION
For the recent years, fixed and floating offshore wind turbine have been of particular interest from both scientific andindustrial communities. A full understanding of wind turbines
wakes is crucial to improve their aerodynamical performances
when operating in wind farms (Schmidt & Stoevesandt, 2015;
Bastine et al., 2018). The optimization of offshore wind farms
is important as the space with wind resources is limited. For
offshore wind turbines embedded in wind farms, multiple dynamics and phenomena impact the wake characteristics, including the influence of the incoming atmospheric boundary
layer, the wake dynamics itself and the effect of the waveinduced surge-motion. In particular, the influence of the surgemotion due to the structure movement of a floating wind turbine, and the consideration of a realistic turbulent boundary
layer have recently been touched on (Fu et al., 2019; Schliffke
et al., 2020; Wise & Bachynski, 2020). Even if large-eddy simulation (LES) approaches have been employed increasingly inthe previous years for these complex modes, the computational
cost of these simulations is still prohibitive for practical applications (Bastine et al., 2018).
For onshore wind turbines, wake models exist in the literature (Heemst, 2015). Simple models are based on the velocity deficit, which could include turbine additional turbulence
and wake meandering (Jensen, 1983; Ainslie, 1988; Frandsen
et al., 2006). More complex wake models have been developed using CFD (Frandsen et al., 2006), but they are considered lacking of physical representativity compared with exper-

EXPERIMENTAL SET-UP
Experiments were carried in the LHEEA’s atmosphericwind tunnel. The experimental set-up is presented in Fig. 1.
The wind turbine is modeled using a porous disk of diameter
D = 0.16 m. The disk center is set at a height zhub = 0.12m with respect to the floor. The model represents the floating1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022(a)Figure 1.

(b)
Experimental set-up: (a) picture of the set-up in the wind-tunnel and (b) schemes of the set-up.

2MW wind turbine used in the FLOATGEN research project,installed at Centrale Nantes’ offshore test site in Le Croisic,France. The thrust coefficient Ct is estimated to be approximately 0.5 and the power coefficient C p ≈ 0.25 (Schliffke
et al., 2020). For streamwise positions x/D in the wake further
than 3, the use of porous disks for the characterization of windturbines wakes is considered valid (Schliffke et al., 2020).
Without model, the free-stream velocity is U∞ = 4.2 m/s andthe turbulent intensity about 0.5%. The incoming boundary
layer thickness is δ = 0.6 m and the resulting Reynolds number is Re = U∞ δ /ν ≈ 150000.
To replicate realistic behaviors of floating wind turbines
under wave swell, a sinusoidal surge-motion is imposed on
the model using a linear actuator (Schliffke et al., 2020). The
sinusoidal amplitude is ± 0.01 m and the frequencies tested
fm = [0, 2, 3, 3.75] Hz. The model position is controlled
retroactively and monitored, with a bias of about 1 mm between the expected and real positions (Schliffke et al., 2020).
The wake is characterized with Stereoscopic PIV (SPIVor PIV 2D3C) in a y − z plane normal to the main flow direction at two streamwise positions x/D = 4.6 and 8.1 downstream of the wind turbine model. The range of the final regionof interest is about 3D × 2D along these directions. The sampling frequency is fPIV = 14.1 Hz and 14000 snapshots wereacquired for each case. Constant temperature anemometry(CTA) measurements were also performed simultaneously to
the Stereo-PIV. Twelve HWA sensors are distributed spanwise,
downstream the PIV measurement plane and at two heights(0.47D and 1.25D). The sampling frequency for the HWA is
FHWA = 15 kHz. Sensors were calibrated using a King’s law
by measuring the free-stream flow with the help of a Pitot tube.
These HWA acquisitions were considered, in addition to thewake documentation with means statistics and spectral analysis, to perform the linear stochastic estimation of time-resolved
velocity fields.

2.5

z/D

2.0
1.5
1.0
0.5
0.0 0.7

1.0−0.03 0.00

U /U∞

0.03

−0.03 0.00

V /U∞

0.03

W /U∞

2.5

z/D

2.0
1.5
1.0
0.5
0.00.05

0.10

σu/U∞

0.00

0.05

σv /U∞

0.00

0.05

σw /U∞

Figure 2. Mean U/U∞ (first line) and RMS velocities σu /U∞(second line) at y/D = 0 for the three spatial components forthe turbulent boundary layer without model. Scales are significantly different between the streamwise velocity and the othervelocity components.

also valid for the 1 / 750 scaled model. The streamwise turbulence intensity Iu fits well with the VDI database, when the
spanwise and wall-normal components Iv and Iw are underestimated by a third.
The mean wake flow is also documented with these measurements. Streamwise mean and RMS velocity fields are presented in Fig. 3. Two streamwise positions in the wake arepresented here: x/D = 4.6 and 8.1. The mean flow in the nearwake is disturbed by the disk, following its shape (represented
with dash line in Fig. 3). At x/D = 8.1, the wake center isslightly shifted to the negative y-direction, also seen in previous works (Schliffke et al., 2020; Foti et al., 2019). It could
correspond to the small spanwise velocity of the incoming flow
observed previously. Compared to the flow without model, theturbulence intensity increases in the near-wake from 8 % up to
15 %. The circular horseshoe shape in the near-wake has beenfound in previous works (Hamilton et al., 2018). The slightshift in the negative y-direction is observed to the RMS fields

MEAN FLOW
The present study is first used to document the mean flow
without model and the wake. The mean and RMS velocitiesof the atmospheric turbulent boundary layer without model
are presented in Fig. 2. Profiles of the three components
along the wall-normal direction z/D going through the disk
center (y/D = 0) are considered here. Mean streamwise velocity U/U∞ corresponds to a turbulent boundary layer profileand from previous works in this wind tunnel (Schliffke et al.,2020). A small negative spanwise velocity V /U∞ ≈ 1 % is also
observed for the turbulent boundary layer. It has been observedin previous works and could be linked to large flow structuresdeveloping upstream the measurement region.
The comparison of the turbulence intensities with the German VDI requirements (VDI, 2017), already applied by Schliffke et al. (2020) for the current turbulent boundary layer, is2

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

1.5

0.10

1.0

0.05

0.5
−1

0
y/D

0.00

1

u

0.15

∞

0.15

1.5

0.10

1.0

0.05

0.5
−1

0
y/D

1

POD MODES

0.00(b) X/D = 8.1

Cumul. eigenvalues (x/D = 4.6)

Cumul. eigenvalues (x/D = 8.1)

100

100

λi

(a) X/D = 4.6

2.0

∞
P

TBL
0 Hz
2 Hz
3 Hz
3.75 HziP

λi /Figure 3. Streamwise mean U/U∞ (first line) and RMS velocity σu /U∞ (second line) for: (a) wake for the fixed modelat x/D = 4.6 and (b) wake for the fixed model at x/D = 8.1.
Dash lines correspond to the position of the porous disk in the
Y − Z plane.

10−1

0

20

TBL
0 Hz
2 Hz
3 Hz
3.75 Hz

10−1

40

0

(a)

(b)

METHODOLOGY OF THE RECONSTRUCTIONUSING POD-mLSE
Spatial velocity fields measured by PIV and synchronizedtime-resolved velocity measurements using HWA are combined for the reconstruction of the full spatio-temporal dynamics using a multi-time-delay Proper Orthogonal Decomposition and Linear Stochastic Estimation (POD-mLSE) approach(Durgesh & Naughton, 2010). Velocity fields are decomposed
into temporal and spatial modes using the classical snapshots
POD:

The main results of the POD analysis are presented here.
iwith Nm the number of modes selected for the truncature.
Here, Nm = 100 modes are chosen, corresponding to about
80% of the cumulative eigenvalues energy. The objective isto determine the more suitable coefficients Bi jk to express therelation between the temporal modes ai and the HWA sensors
with time delays τk :

2.0

Nk

2.0

0.01

1.5

−0.01

0.0

y/h

0.5

1.0

−0.02

Spatial mode ΦU # 01

Spatial mode ΦU # 02

0.01

1.5
0.00

1.0
0.5
−1.0 −0.5

2.0

0.01

0.0

y/h

0.5

1.0

−0.01

0.00

1.0
0.5
−1.0 −0.5

0.0

y/h

0.5

1.0

−0.01

Figure 5. Example of spatial modes Φi maps for modes i =0 to 2 (columns) for the fixed model ( fm = 0 Hz) at x/D = 4.6.

An example of the spatial modes Φi is presented in Fig. 5.
The dipole-like pairs (modes 0 and 1, oriented respectively inthe spanwise and wall-normal direction) and quadripole-likepairs (mode 2 and 3, not shown here), are similar to the ones
obtained for similar configurations (Andersen et al., 2013;
Bastine et al., 2014). The symmetry of modes pairs corresponds to an invariance of the flow under rotations (Berkooz
et al., 1993; Bastine et al., 2014). However, symmetry of the(3)with C{ai , S jk } the cross-correlations between the temporalmodes and the sensors with delays, and C{S jk } the correlations
between the different sensors with different delays. Temporalmodes abi are therefore estimated at higher temporal resolution

0.02

0.00

1.0
0.5
−1.0 −0.5

with N j = 12 the number of HWA sensors S j and Nk the number of delays imposed on the sensors. Here, Nk = 21 delays are
distributed between ±1 s, following previous reconstruction
parameters on similar experiments (Blackman & Perret, 2016).
The coefficients Bi jk are determined through the resolution ofa least-square minimization problem using cross-correlations:−1
C{S jk }Bi jk = C{ai , S jk }Spatial mode ΦU # 00

1.5

z/h

∑

j=0 k=0

(2)

z/h

(1)

i=0

Bi jk S j (t − τk )∞The convergence using the cumulative eigenvalues ∑ λi / ∑ λi
is first shown in Fig. 4. The two streamwise positions in thewake are considered, and compared with the POD modes forthe turbulent boundary layer without model. Compared withtypical bluff-body flows, the eigenvalues convergence is relatively slow, due to the high Reynolds number incoming turbulent boundary layer. The eigenvalues are therefore comparable with previous works, in particular De Cillis et al. (2021):
for a near-wake flow downstream a nacelle and tower model,
the cumulative eigenvalues reached about 40 % after Nm = 15
modes, as it is about 50 % for the present study for the sameamont of modes.

Nm

Nj

∞

Figure 4. Cumulative eigenvalues ∑ λi / ∑ λi from the POD
obtained from different streamwise positions (a) x/D = 4.6
and (b) x/D = 8.1. For each configuration, four frequencies
of motion fm are presented in solid lines: 0 Hz (fixed), 2 Hz,
3 Hz and 3.75 Hz. TBL without model is presented in dottedline.

at x/D = 8.1.

ai (t) = ∑

40

Nm

i

u(x,t) ≈ ∑ ai (t) Φi (x)

20

Nm

z/h

z/D

∞

0
1
y/D σ /URMS velocity

λi

u

2.0

0.0

−1

∞
P

0
1
y/D σ /URMS velocity

1.0
0.5

1.0
0.5

0.0

−1

1.5

using Eq. 2, then combined with the spatial modes using POD(Eq. 1) to reconstruct the velocities. Two flow configurations
considered for reconstruction are presented here, as important
cases for their implementation in aeroelastic simulations: theturbulent boundary layer alone and the fixed model wake immersed in the turbulent boundary layer at x/D = 8.1. The sampling frequency used for the reconstruction is Fs = 7.05 kHz,to meet the conditions required for these simulations.

λi /

0.5

Mean velocity U /U∞

i
P

0.5

1.0

2.0
z/D

1.5

1.0

z/D

z/D

2.0

Mean velocity U /U∞3

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
on the wake. For example, a motion at frequency fm = 2 Hz
shows similar dynamical behavior than the fixed model, where
motions of fm = 3 and 4 Hz shows the emergence of substantial peaks and increase of the spectral energy at low frequency.

mode 1 is slightly broken in the wall-normal due to the incoming boundary layer, which is not always taken into account instudies.

0.00
−0.01

−0.01

−0.02

−0.02

−0.02

0

−0.03

1

y/D

−1

0

−0.03

1

y/D

−1

0

RECONSTRUCTION
Few results of the reconstruction of the velocity fields arepresented here. Only the turbulent boundary layer and the farwake for the fixed model are shown here, but the stochastic
estimation was performed for the full database.

1y/D

X/D = 4.6

0.01

−0.01

0.00

−0.03

1

0.00

TBL

−0.02
−1

0

−0.03

1

y/D

TBL

2

−0.01

−1

0

2

1

y/D

0

b
a0 /

0

y/D

0 Hz
2 Hz
3 Hz
3.75 Hz

0.01

−0.02
−1

ΦU at z/D =0.75 # 02

0.02

−0.01

−0.02
−0.03

0.03
0 Hz
2 Hz
3 Hz
3.75 Hz

2λ00.00

ΦU at z/D =0.75 # 01

0.02

√

0.01

ΦU

0.03
0 Hz
2 Hz
3 Hz
3.75 HzΦU

ΦU at z/D =0.75 # 00

ΦU

0.03
0.02

2λ1

−1

0 Hz
2 Hz
3 Hz
3.75 Hz

0.00

−0.01
−0.03

ΦU at z/D =0.75 # 02

0.02
0.01

√

0.03
0 Hz
2 Hz
3 Hz
3.75 HzX/D = 8.1

−2

Figure 6. Profiles of spatial modes Φi for two streamwise
positions and along the spanwise y direction at the hub heightz/D = 0.74 for modes i = 0 to 2 (Raibaudo et al., 2022).

−2

a0 /

0√

−2

2
2λ0

0.4

f ⋆ Φuuf ⋆ Φuu

0.2

10−2

10−1

f ⋆ = f D/Uhub

0.2

0.0

0.4
0 Hz
2 Hz
3 Hz
3.75 Hz

0.1

0.1
0.0

PSD (x/D = 4.6) # 00

0.3

10−1

f ⋆ = f D/Uhub

0.0

10−2

2λ1
√

b
a1 /

b
a0 /
−2

0

a0 /

0√

−2

2
2λ0

−2

a1 /

0√

2
2λ1

A firstpcomparison of the first reconstructed temporalmodes abi / 2λi , with λi the POD eigenvalue of mode i, isperformed in Fig. 8. These reconstructed modes abi are compared to the original modes ai : strong correlation is observed
for both chosen configurations, suggesting the reconstruction
is consistent. It can be observed the distribution is more scattered for the reconstruction of the wake than for the turbulent
boundary layer, implying more difficulties to capture the flow
complexity of the wake.

0.1
10−2

2
2λ1

Figure 8. Scatter
temp plots for the first two reconstructedpporal mode abi / 2λi versus original mode ai / 2λi at two
streamwise positions: (a-b) turbulent boundary layer withoutmodel, (c-d) x/D = 8.1.

0 Hz
2 Hz
3 Hz
3.75 Hz

0.2

0√WAKE - x/D = 8.1

0−2

PSD (x/D = 8.1) # 00

0.3

a1 /

2

2λ0
√
PSD (TBL) # 00

f ⋆ Φuu

0.4−2

WAKE - x/D = 8.1

2

Profiles of the spatial modes ΦU of the streamwise velocity component for two streamwise positions and along the
spanwise y-direction are presented in Fig. 6. Profiles are considered at the hub height (z/D = 0.74) and for different frequencies of surge-motion. Modes signs are adapted for a better comparison. A more complete analysis of the POD modes
for the floating wind turbine can be found in Raibaudo et al.
(2022). No significant influence of the surge-motion can befound in the spatial modes. Profiles are close in amplitude andshape. Same observations can be performed for the other velocities components v and w.

0.3

0

b
a1 /

0.00

ΦU at z/D =0.75 # 01

0.02
0.01

10−1

f ⋆ = f D/Uhub

Figure 7. Premultiplied PSD of the temporal modes ai obtained from different configurations: (a) turbulent boundary
layer without model, (2) model wake at x/D = 4.6 and (3)model wake at x/D = 8.1 (Raibaudo et al., 2022).

z/D

2

However, as detailed in Raibaudo et al. (2022), significant
differences can be observed on the temporal modes. Premultiplied PSD of the temporal modes ai are presented in Fig. 7 forthree configurations (TBL and the two streamwise positionsin the wake). Non-dimensionalized frequency f ∗ = f D/Uhub
is used here to dimensionalize the PSD, as performed in previous works, with Uhub = 3.8 m/s the velocity at the hub position
without model.
A broad spectrum is found for the flow without model,
centered around the main reduced frequency ( f ∗ = 0.04 orf ≈ 1 Hz). By considering the porous disk wake without motion, the spectra amplitude increases significantly and the mainfrequency is shifted to f ∗ = 0.13 ( f ≈ 3 Hz). Eventually, thesurge-motion imposes the dynamics of the wake. In particular,
the higher surge-motion frequencies have a greater influence

RMS profiles (TBL)

2
σu
σv
σw

1
0
0.00

0.02
0.04
σ/U∞

0.06

z/D

ΦU

0.03
0 Hz
2 Hz
3 Hz
3.75 HzΦU

ΦU at z/D =0.75 # 00

ΦU

0.03
0.02
0.01

RMS profiles (x/D = 8.1)
σu
σv
σw

1
0
0.00

0.02
0.04
σ/U∞

0.06

Figure 9. RMS reconstructed velocity u/U∞ profiles alongz using mtd-POD-LSE and original velocity using the sameamount of modes Nm = 100. (a) TBL and (b) fixed model at
x/D = 8.1. dots: truncated original PIV data, lines: mtd-PODLSE data

Reconstructed RMS velocity profiles along z are shownin Fig. 9. These reconstructed velocities are compared withthe original velocities obtained by the POD truncature (Eq. 1)

4

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022with the same amount of modes Nm = 100 used for the mtdPOD-LSE process. For the turbulent boundary layer (Fig. 9(a)), the streamwise and normal terms, respectively u/U∞ and
w/U∞ , are well reconstructed. Only the spanwise component
v/U∞ is underestimated of about 30% in average over the profile, more importantly far from the wall. Same analysis can bedone for the reconstruction of the model wake at x/D = 8.1(Fig. 9 (b)). All reconstructed velocities components are consistent with the original velocities. However, the reconstructedvelocities are underestimated between 4% for u/U∞ to 15%
for w/U∞ . Even if the stochastic estimation looses information similarly to the TBL, these differences could be linked
to the conditioning of the correlation matrix during the POD
process and could be improved by using Tikhonov regularization for example. The presence of the model generates a more
pronounced three-dimensional wake which is captured by the
SPIV but not well by the one-dimensional hot-wires.

PSD (TBL)

10−2

10−4
10−6
−8

10

10−2

f + Φuuf + Φuu

10−2

REC.
PIV
HWA

10−1

f+

101

102

REFERENCES
Ainslie, J.F. 1988 Calculating the flowfield in the wake of windturbines. Journal of Wind Engineering and Industrial Aerodynamics 27 (1-3), 213–224.
Andersen, Søren Juhl, Sørensen, Jens Nørkær & Mikkelsen,
Robert 2013 Simulation of the inherent turbulence and wakeinteraction inside an infinitely long row of wind turbines.
Journal of Turbulence 14 (4), 1–24.
Andersen, S. J., Sørensen, J. N. & Mikkelsen, R. 2014 Reduced order model of the inherent turbulence of wind turbine wakes inside an infinitely long row of turbines. Journalof Physics: Conference Series 555 (1).
Bachynski, Erin E. & Eliassen, Lene 2019 The effects of coherent structures on the global response of floating offshore
wind turbines. Wind Energy 22 (2), 219–238.
Bastine, David, Vollmer, Lukas, Wächter, Matthias & Peinke,
Joachim 2018 Stochastic wake modelling based on POD
analysis. Energies 11 (3), 1–29.
Bastine, D., Witha, B., Wächter, M. & Peinke, J. 2014 POD
analysis of a wind turbine wake in a turbulent atmosphericboundary layer. Journal of Physics: Conference Series
524 (1).
Bastine, David, Witha, Björn, Wächter, Matthias & Peinke,
Joachim 2015 Towards a simplified dynamic wake modelusing POD analysis. Energies 8 (2), 895–920.
Berkooz, Gal, Holmes, Philip & Lumley, John L 1993
ProOrthDecHydroAnnurev1993.pdf. Annual Review of
Fluid Mechanics (25), 539–575.
Blackman, Karin & Perret, Laurent 2016 Non-linear interactions in a boundary layer developing over an array of cubes
using stochastic estimation. Physics of Fluids 28 (9).
De Cillis, Giovanni, Cherubini, Stefania, Semeraro, Onofrio,
Leonardi, Stefano & De Palma, Pietro 2021 POD-based
analysis of a wind turbine wake under the influence of tower
and nacelle. Wind Energy 24 (6), 609–633.
Durgesh, V. & Naughton, J. W. 2010 Multi-time-delay LSEPOD complementary approach applied to unsteady highReynolds-number near wake flow. Experiments in Fluids
49 (3), 571–583.
Foti, Daniel, Yang, Xiaolei, Shen, Lian & Sotiropoulos, Fotis
2019 Effect of wind turbine nacelle on turbine wake dynamics in large wind farms. Journal of Fluid Mechanics 869,
1–26.
Frandsen, Sten, Barthelmie, Rebecca, Pryor, Sara, Rathmann,Ole, Larsen, Søren, Højstrup, Jørgen & Thøgersen, Morten
2006 Analytical modelling of wind speed deficit in large
offshore wind farms. Wind Energy 9 (1-2), 39–53.
Fu, Shifeng, Jin, Yaqing, Zheng, Yuan & Chamorro,
Leonardo P. 2019 Wake and power fluctuations of a model
wind turbine subjected to pitch and roll oscillations. Applied
Energy 253 (February), 113605.
Hamilton, Nicholas, Viggiano, Bianca, Calaf, Marc, Tutkun,
Murat & Cal, Raúl Bayoán 2018 A generalized framework
for reduced-order modeling of a wind turbine wake. WindPSD (x/D = 8.1)

10−4
10−6
−8

10
100

The reconstructed fields will now be implemented in anaero-elastic code for the estimation of the forces applied on
the real scale wind turbine. Not detailed here, but during thepresentation and in a future publication, the influence of thehigh-frequencies surge-motions of the floating wind turbine
will strongly impact the mean and RMS forces obtained withthese calculus. The importance of a realistic flow dynamics
consideration for the study of floating wind turbines is therefore confirmed.

10−2

REC.
PIV
HWA

10−1

100

f+

101

102

Figure 10. Premultiplied PSD of the reconstructed velocities
at the hub position, compared to the PIV and HWA. (a) TBL
and (b) fixed model at x/D = 8.1. The vertical dashed line
corresponds to the PIV sampling frequency limit.

Spectral analysis is also performed on the reconstructed
streamwise velocity and presented in Fig. 10. PSD are compared with the ones done with the original velocity with thesame amount of modes and on a hot-wire sensor (n◦ 10 at
y/D = 0 and z/D = 1.25). Spectrum is consistent at low frequency with the PIV and follows well the dynamics behaviorof hot-wire sensor. A loss of spectrum amplitude is also observed between the two, suggesting a loss of information at
higher frequency with the process due to the POD truncatureand the limited number of sensors, for example.
PSD of the reconstructed velocities are also consistent
with the spectral analysis on the PIV and HWA. Spectra
have more amplitude at low frequency, with peaks at f + =O(10−1 ), and reconstructed velocity PSDs also catch this behavior at lower frequency.

CONCLUSIONS AND PERSPECTIVES
Considering realistic conditions of the incoming flows ofwind turbines has been proven to be of crucial importance. In
the present study, velocity fields have been obtained experimentally for the turbulent boundary layer and wakes of fixed
and moving porous disk corresponding to realistic behaviors ofoffshore wind turbines. The velocity has been reconstructed athigh temporal resolution using mtd-POD-LSE. The influenceof the surge-motion on the POD modes has been presented
here, and detailed in a previous article. The spatial modes
show no significant difference due to the motion, when thetemporal modes includes the spectral signature of the surgemotion. In particular, higher surge-motion frequencies showsthe emergence of strong peaks on the PSDs. Spatio-temporal
dynamics of the wake flow has been shown to be well capturedby this low-order representation of the turbulent flow.

512th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
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