unsteady case compared to the fixed-bottom one, which indi-
cates a faster wake recovery (see Fig. 18).

Both FVW and CFD predict larger oscillation amplitudes
compared to the experimental results, indicating that the ef-
fect of the platform motion on the wake is overestimated for
both simulation methodologies.

The effect of platform motion on the wake can also be ob-
served in terms of wake deficit (see Sect. 6.2), as the varia-
tion in rotor loading affects the amount of energy extracted
from the wind and hence the velocity deficit in the wake. Fig-
ure 15 shows the wake deficit oscillations during a cycle of
surge motion for LC 2.5. Indeed, the motion of the rotor does
not only induce a velocity oscillation in specific points of
the wake, but the effect is also visible when considering the
wake deficit, which includes the contributions from all the
crosswind probes. Both the experimental and the simulation
results oscillate around the fixed-bottom value, represented
by the red diamonds. Therefore, the differences observed be-
tween the average wake deficit values from the experimental
and simulation results are not induced by inaccurate wake
modeling during platform motion. As has already been ob-
served by Bergua et al. (2023), the FVW results probably
differ because of the different wake lengths imposed dur-
ing the simulations (Table 3). Indeed, if the wake recovery
happens closer to the rotor, the recorded wake deficit will
be lower and vice versa. As was the case for the streamwise
velocity oscillations, all simulation approaches predict larger
amplitudes of the oscillations of the wake deficit compared
to the experimental results. In terms of phase shift, most sim-
ulation results show the minimum value of the wake deficit
in advance in comparison to the experimental results. The
phase of the wake deficit is a function of the propagation
speed of the velocity oscillations, which in turn is related to
the average steady-state wake deficit (represented by the red
diamonds in Fig. 15b). The significant differences observed
among the participants in terms of steady-state wake deficit
could explain the discrepancies observed in terms of phase
shift.

8.2 LC summary

The analysis of the wake deficit oscillations carried out in
the previous section was repeated for all the LCs, and the re-
sults are shown in Fig. 16. According to the linearized quasi-
steady theory (see Sect. 1), the amplitude of the wake deficit
oscillations should increase linearly as a function of the fre-
quency of platform motion. Indeed, the experimental wake
deficit measured on the cross-plane line follows the quasi-
steady linear trend, but some differences are observed in the
simulation results. In fact, the majority of the FVW and CFD
simulations predict a sharp increase in the wake deficit oscil-
lations (due to an increase in the streamwise velocity oscilla-
tions) for LC 2.7. TNO and POLIMI show the closest results
to the experimental data for LCs 2.1 and 2.5, but a similar
sharp increment is observed for LC 2.7.

This difference between the experimental and simulation
results is not justified by a similar increase in rotor thrust for
LC 2.7 (see Fig. 16b), suggesting that the oscillations in the
wake deficit are caused by the amplification of wake instabil-
ities. As noted by Kleine et al. (2022), the platform motion
may excite vortex instabilities and cause the interaction of
multiple vortices downstream, which result in large velocity
oscillations. This effect should be more pronounced when
the frequency of platform motion is half of the rotational
frequency of the rotor (as is the case for LCs 2.7 and 3.7)
(Kleine et al., 2022). However, the experimental data do not
show a similar increase in the velocity oscillations for the
tested LCs, and the wake deficit oscillations follow the lin-
earized quasi-steady theory. Hence, the simulations might
overpredict the growth of such instabilities. These differ-
ences could be related to unsteadiness in wind tunnel inflow,
which are not captured by simulations and might dampen or
modify the effect of these instabilities in the experimental re-
sults. However, this aspect was not investigated in the current
study. Additionally, further experimental tests are required to
confirm the available experimental data as, due to the limited
number of data points available, error bars for the amplitude
of the wake deficit of the experimental data could not be in-
cluded.

Comparing the surge and pitch results (Fig. 16c and d), all
participants predict similar wake deficit amplitudes between
the two types of platform motions. Additionally, the increase
in wake deficit amplitudes shown at the highest frequency of
surge motion is also present for the pitch motion, suggesting
that the far-wake response is similar for the two cases.

The wake response to the surge platform motion can be
observed in Fig. 17, where the amplitude of the streamwise
velocity oscillations calculated from each of the along-wind
HWAs is shown as a function of rotor distance. The plots
are presented only for the surge cases for brevity, but the
pitch load cases provide analogous results. By comparing
the velocity oscillations for increasing reduced frequency, the
amplification of wake instabilities can be clearly observed.
For the experimental results, the amplitude is almost con-
stant and does not show a significant rise with increasing
distance from the rotor for all LCs. With increasing reduced
frequency, from LC 2.1 to LCs 2.5 and 2.7, the amplitude
of the velocity oscillations grows by approximately 2 times.
Among the simulation results, most participants predict sim-
ilar amplitudes for LC 2.1 (Fig. 17a). However, for LC 2.5
and especially for LC 2.7, only CENER, TNO, and POLIMI,
show comparable amplitudes to the experiments. The rest of
the participants predict a significant increase (up to 1 order
of magnitude) in the oscillation amplitude, independently of
the methodology used. Additionally, large differences are ob-
served across the participants, as the entity of the velocity os-
cillation varies from a maximum of 0.33 m s⁻¹ to a minimum
of 0.06 m s⁻¹.

Finally, Fig. 18 shows the average streamwise velocity
value as a function of rotor distance for both surge and pitch
<figure><img src="image_15.png" /><figcaption>**Figure 14.** (a) Streamwise velocity oscillations during platform motion from a single HWA probe at *x* = 5.48 m and *y* = 0.9 m for LC 2.5. The dashed lines represent the FVW results, and the solid lines represent either CFD or experimental results. The shaded area represents the standard deviation of the experimental data. (b) Amplitude of the streamwise velocity oscillations calculated at the frequency of platform motion. The red lines represent the average values during the cycle of motion, and the red diamonds represent the fixed-bottom case.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**Figure 15.** (a) Wake deficit oscillations during platform motion for LC 2.5. The dashed lines represent the FVW results, and the solid lines represent either CFD or experimental results. The shaded area represents the standard deviation of the experimental data. (b) Amplitude of the wake deficit oscillations at the frequency of platform motion. The red lines represent the average wake deficit during the cycle of motion, and the red diamonds represent the fixed-bottom value.</figcaption></figure>

cases. The experimental surge cases show that the wake re-
covery happens at about *x* ≈ 3.5 m from the rotor. The lo-
cation of the velocity minimum and the velocity trend are
not affected by the surge motion, independent of the re-
duced frequency. Indeed, almost no difference is observed
with the fixed-bottom case, which was presented by Bergua
et al. (2023). Only the FVW simulations by EURE and UPC

show the wake recovery at a similar distance from the rotor,
whereas for the rest of the participants the velocity minimum
is not observed before the last along-wind HWA. The differ-
ences observed across the FVW participants are most likely
due to the imposed wake length in the simulation, which will
affect the wake recovery. Despite this, all simulations show
that the surge motion only has a minimal impact on the wake
<figure><img src="image_15.png" /><figcaption>**Figure 14.** (a) Streamwise velocity oscillations during platform motion from a single HWA probe at *x* = 5.48 m and *y* = 0.9 m for LC 2.5. The dashed lines represent the FVW results, and the solid lines represent either CFD or experimental results. The shaded area represents the standard deviation of the experimental data. (b) Amplitude of the streamwise velocity oscillations calculated at the frequency of platform motion. The red lines represent the average values during the cycle of motion, and the red diamonds represent the fixed-bottom case.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**Figure 15.** (a) Wake deficit oscillations during platform motion for LC 2.5. The dashed lines represent the FVW results, and the solid lines represent either CFD or experimental results. The shaded area represents the standard deviation of the experimental data. (b) Amplitude of the wake deficit oscillations at the frequency of platform motion. The red lines represent the average wake deficit during the cycle of motion, and the red diamonds represent the fixed-bottom value.</figcaption></figure>

cases. The experimental surge cases show that the wake re-
covery happens at about *x* ≈ 3.5 m from the rotor. The lo-
cation of the velocity minimum and the velocity trend are
not affected by the surge motion, independent of the re-
duced frequency. Indeed, almost no difference is observed
with the fixed-bottom case, which was presented by Bergua
et al. (2023). Only the FVW simulations by EURE and UPC

show the wake recovery at a similar distance from the rotor,
whereas for the rest of the participants the velocity minimum
is not observed before the last along-wind HWA. The differ-
ences observed across the FVW participants are most likely
due to the imposed wake length in the simulation, which will
affect the wake recovery. Despite this, all simulations show
that the surge motion only has a minimal impact on the wake
<figure><img src="image_17.png" /><figcaption>**Figure 16.** Amplitude of normalized wake deficit oscillations as a function of reduced frequency and rotor thrust for surge (a, b) and pitch cases (c, d). The dashed lines represent the FVW results, and the solid lines represent either CFD or experimental results.</figcaption></figure>

recovery, for all the reduced frequencies analyzed. However, this is not the case for the pitch cases, where the average velocity decreases faster and recovers slower at higher reduced frequency for most of the participants. The trend cannot be validated through experimental data, but it is consistent across the various simulation methodologies. As has already been observed during the analysis of tip vortices, the pitch motion of the platform seems to affect the behavior of the wake more profoundly than it affects surge cases.

## 9 Conclusions

During the OC6 project, the participants modeled a scaled model of the DTU 10 MW rotor under fixed-bottom, surge, and pitch motion conditions using several numerical approaches with varying levels of fidelity. Simulations were also benchmarked against experimental data obtained during wind tunnel tests by POLIMI. The present study analyzes the

characteristics of the near wake (i.e., from 0.25 to 0.5 D) and far wake (i.e., from 0.9 to 2.3 D) of the rotor, with special focus on the propagation of tip vortices in the near wake.

In the fixed-bottom case, all simulation approaches agree by 0.03 D with each other in terms of the tip vortex position, and results are consistent with experimental data. The connection velocity calculated from most FVW and CFD simulations falls within 1 standard deviation of the experimental data, with maximum differences of about 10%. In terms of the tip vortex strength, the FVW methods can correctly predict the strength reduction over time; however, differences of up to 20% are observed between the participants. The CFD ALM simulations underpredict the strength to up to 20% despite the increased computational cost. Larger differences were observed in terms of the core radius for both FVW and CFD approaches, which indicates some improvements can still be made in predicting this metric. Indeed, for FVW methods this parameter may depend on the blade discretiza-
<figure><img src="image_17.png" /><figcaption>**Figure 16.** Amplitude of normalized wake deficit oscillations as a function of reduced frequency and rotor thrust for surge (a, b) and pitch cases (c, d). The dashed lines represent the FVW results, and the solid lines represent either CFD or experimental results.</figcaption></figure>

recovery, for all the reduced frequencies analyzed. However, this is not the case for the pitch cases, where the average velocity decreases faster and recovers slower at higher reduced frequency for most of the participants. The trend cannot be validated through experimental data, but it is consistent across the various simulation methodologies. As has already been observed during the analysis of tip vortices, the pitch motion of the platform seems to affect the behavior of the wake more profoundly than it affects surge cases.

## 9 Conclusions

During the OC6 project, the participants modeled a scaled model of the DTU 10 MW rotor under fixed-bottom, surge, and pitch motion conditions using several numerical approaches with varying levels of fidelity. Simulations were also benchmarked against experimental data obtained during wind tunnel tests by POLIMI. The present study analyzes the

characteristics of the near wake (i.e., from 0.25 to 0.5 D) and far wake (i.e., from 0.9 to 2.3 D) of the rotor, with special focus on the propagation of tip vortices in the near wake.

In the fixed-bottom case, all simulation approaches agree by 0.03 D with each other in terms of the tip vortex position, and results are consistent with experimental data. The convection velocity calculated from most FVW and CFD simulations falls within 1 standard deviation of the experimental data, with maximum differences of about 10%. In terms of the tip vortex strength, the FVW methods can correctly predict the strength reduction over time; however, differences of up to 20% are observed between the participants. The CFD ALM simulations underpredict the strength to up to 20% despite the increased computational cost. Larger differences were observed in terms of the core radius for both FVW and CFD approaches, which indicates some improvements can still be made in predicting this metric. Indeed, for FVW methods this parameter may depend on the blade discretization.
<figure><img src="image_18.png" /><figcaption>**Figure 17.** Amplitude of streamwise velocity oscillations at the frequency of platform motion calculated from each of the along-wind probes as a function of rotor distance for the analyzed surge cases. (a) LC 2.1: A = 0.125 m, $f_r$ = 0.071; (b) LC 2.5: A = 0.035 m, $f_r$ = 0.568; (c) LC 2.7: A = 0.008 m, $f_r$ = 1.137. The dashed lines represent the FVW results, and the solid lines represent either CFD or experimental results.</figcaption></figure>

tion used as well as other simulation parameters such as the initial core radius. Careful consideration of these parameters should be carried out when analyzing the tip vortex behavior. In CFD ALM results, the core radius is overpredicted by all the participants, which underlines a limitation of this approach that could also affect its reliability in wake modeling. These results show how correctly tuned FVW methodologies can capture the behavior of the tip vortices at a fraction of the cost of CFD methods.

For unsteady cases, the effect of platform motion on the tip vortex position and strength was evaluated. In surge cases, simulations showed good agreement when the reduced frequency is less than 0.5, with the results oscillating around the steady-state fixed-bottom value as predicted by the lin-

earized quasi-steady theory. However, results diverge from the expected quasi-steady behavior when the reduced frequency increases.

Additionally, the differences across both FVW and CFD approaches increase in those cases, underlining how efforts are probably required to tune the currently available methodologies in order to correctly predict the position and strength of the tip vortices shed from a floating wind turbine under surge motion. Similar conclusions can be drawn when a pitch motion is imposed. Under this condition, however, additional discrepancies between the participants were observed at low frequencies of motion, when the largest tilt angles of the rotor are reached. Additional PIV campaigns are recommended to better understand the evolution of tip vortex strength and
<figure><img src="image_18.png" /><figcaption>**Figure 17.** Amplitude of streamwise velocity oscillations at the frequency of platform motion calculated from each of the along-wind probes as a function of rotor distance for the analyzed surge cases. (a) LC 2.1: $A = 0.125$ m, $f_r = 0.071$; (b) LC 2.5: $A = 0.035$ m, $f_r = 0.568$; (c) LC 2.7: $A = 0.008$ m, $f_r = 1.137$. The dashed lines represent the FVW results, and the solid lines represent either CFD or experimental results.</figcaption></figure>

tion used as well as other simulation parameters such as the initial core radius. Careful consideration of these parameters should be carried out when analyzing the tip vortex behavior. In CFD ALM results, the core radius is overpredicted by all the participants, which underlines a limitation of this approach that could also affect its reliability in wake modeling. These results show how correctly tuned FVW methodologies can capture the behavior of the tip vortices at a fraction of the cost of CFD methods.

For unsteady cases, the effect of platform motion on the tip vortex position and strength was evaluated. In surge cases, simulations showed good agreement when the reduced frequency is less than 0.5, with the results oscillating around the steady-state fixed-bottom value as predicted by the lin-

earized quasi-steady theory. However, results diverge from the expected quasi-steady behavior when the reduced frequency increases.

Additionally, the differences across both FVW and CFD approaches increase in those cases, underlining how efforts are probably required to tune the currently available methodologies in order to correctly predict the position and strength of the tip vortices shed from a floating wind turbine under surge motion. Similar conclusions can be drawn when a pitch motion is imposed. Under this condition, however, additional discrepancies between the participants were observed at low frequencies of motion, when the largest tilt angles of the rotor are reached. Additional PIV campaigns are recommended to better understand the evolution of tip vortex strength and
<figure><img src="image_19.png" /><figcaption>**Figure 18.** Average streamwise velocity as a function of rotor distance for surge and pitch load cases. Panels (a)–(c) show the results from the surge cases: (a) LC 2.1, $f_r = 0.071$; (b) LC 2.5, $f_r = 0.568$; and (c) LC 2.7, $f_r = 1.137$. Panels (d)–(f) show the results from the pitch cases: (d) LC 3.1, $f_r = 0.071$; (e) LC 3.5, $f_r = 0.568$; and (f) LC 3.7, $f_r = 1.137$. The dashed lines represent the FVW results, and the solid lines represent either CFD or experimental results. The shaded area represents the standard deviation of the experimental results.</figcaption></figure>

position in these conditions. Such a campaign should focus on obtaining measurements at higher reduced frequencies, where wake behavior is yet to be properly characterized. Additionally, the measurements could be performed over multiple cycles of platform motion to provide a more reliable description of the wake response.

Upon examination of hot-wire data, the effect of platform motion on the far wake was further analyzed. Surge and pitch motions induce streamwise velocity oscillations in the wake, which could be problematic for downstream machines, as they could increase rotor loading or affect platform stability. At low frequencies of motion (LC 2.1), all simulation methodologies showed that the amplitude of the velocity perturbations in the wake is less than 1% of the freestream value, as is the case for experimental data. However, in LCs 2.7 and 3.7, where the reduced frequency increases up to 1.2, major differences arise between simulation results and experiments. More specifically, most simulations predict a significant increase in the amplitude of velocity oscillations as distance from the rotor increases, even though this trend is not present in the experimental data. Moreover, the codes do not agree on the predicted magnitude of the velocity oscillations. This result suggests that numerical meth-

ods might overpredict the effect of platform motion on the wake. This issue affects all simulation methodologies with varying degrees of severity (up to a factor of 3); hence, it does not seem to be connected with a specific approach. A possible cause of the discrepancy between the experimental data and simulations might be unsteadiness (background turbulence and wall effects) in the wind tunnel inflow, which does not allow these instabilities to grow as they do in the simulations. Higher-fidelity CFD models, able to comprehensively model inflow turbulence, are one of the key topics for future aerodynamic studies on FOWTs, although their computational cost is still very high.

Concerning the wake recovery, both simulations and experiments predict a limited effect of surge motion on the velocity recovery at the analyzed frequencies and amplitudes. Additionally, for a pitch motion of the platform, some simulation methodologies showed a slower recovery of the streamwise velocity, even though no experimental data are available to validate this aspect. Overall, current results suggested that the effect of platform motion on the far wake, differently from original expectations about a faster wake recovery, seems to be very limited or even oriented to the generation of a wake less prone to dissipation.
<figure><img src="image_19.png" /><figcaption>**Figure 18.** Average streamwise velocity as a function of rotor distance for surge and pitch load cases. Panels (a)–(c) show the results from the surge cases: (a) LC 2.1, $f_r = 0.071$; (b) LC 2.5, $f_r = 0.568$; and (c) LC 2.7, $f_r = 1.137$. Panels (d)–(f) show the results from the pitch cases: (d) LC 3.1, $f_r = 0.071$; (e) LC 3.5, $f_r = 0.568$; and (f) LC 3.7, $f_r = 1.137$. The dashed lines represent the FVW results, and the solid lines represent either CFD or experimental results. The shaded area represents the standard deviation of the experimental results.</figcaption></figure>

position in these conditions. Such a campaign should focus on obtaining measurements at higher reduced frequencies, where wake behavior is yet to be properly characterized. Additionally, the measurements could be performed over multiple cycles of platform motion to provide a more reliable description of the wake response.

Upon examination of hot-wire data, the effect of platform motion on the far wake was further analyzed. Surge and pitch motions induce streamwise velocity oscillations in the wake, which could be problematic for downstream machines, as they could increase rotor loading or affect platform stability. At low frequencies of motion (LC 2.1), all simulation methodologies showed that the amplitude of the velocity perturbations in the wake is less than 1% of the freestream value, as is the case for experimental data. However, in LCs 2.7 and 3.7, where the reduced frequency increases up to 1.2, major differences arise between simulation results and experiments. More specifically, most simulations predict a significant increase in the amplitude of velocity oscillations as distance from the rotor increases, even though this trend is not present in the experimental data. Moreover, the codes do not agree on the predicted magnitude of the velocity oscillations. This result suggests that numerical meth-

ods might overpredict the effect of platform motion on the wake. This issue affects all simulation methodologies with varying degrees of severity (up to a factor of 3); hence, it does not seem to be connected with a specific approach. A possible cause of the discrepancy between the experimental data and simulations might be unsteadiness (background turbulence and wall effects) in the wind tunnel inflow, which does not allow these instabilities to grow as they do in the simulations. Higher-fidelity CFD models, able to comprehensively model inflow turbulence, are one of the key topics for future aerodynamic studies on FOWTs, although their computational cost is still very high.

Concerning the wake recovery, both simulations and experiments predict a limited effect of surge motion on the velocity recovery at the analyzed frequencies and amplitudes. Additionally, for a pitch motion of the platform, some simulation methodologies showed a slower recovery of the streamwise velocity, even though no experimental data are available to validate this aspect. Overall, current results suggested that the effect of platform motion on the far wake, differently from original expectations about a faster wake recovery, seems to be very limited or even oriented to the generation of a wake less prone to dissipation.
## Appendix A: Characterization of wind tunnel turbulence

During the experimental campaign the inflow conditions of the wind tunnel were investigated (Fig. A1). Due to the presence of the wind tunnel walls, it was not possible to achieve a perfectly uniform wind speed. However, the velocity was almost constant from about 0.5 m above the wind tunnel floor. The turbulence intensity at the wind tunnel inlet was about 2% above 0.5 m; however values up to 10% are measured near to the ground. The integral length scale in the along-wind direction was about 0.2 m and was almost constant along the wind tunnel height.

<figure><img src="image_20.png" /><figcaption>Figure A1. Characterization of wind tunnel inflow with uncertainty range. (a) Vertical velocity profile normalized by wind speed at hub height, (b) turbulence intensity, and (c) integral length scale.</figcaption></figure>

## Appendix B: Uncertainty in vorticity distribution and tip vortex circulation

The vorticity calculation requires the spatial derivatives of the velocity field. Because both numerical and experimental data are obtained over a discrete grid, a differentiation scheme is required. For example, considering a central differencing scheme, the velocity derivative at a grid point (i, j) along the x direction is calculated as

$$ \frac{\partial f}{\partial x}(i, j) = \frac{f(i+1, j) - f(i-1, jt)}{2\Delta x} + o(\Delta x^2), \quad (B1) $$

where $\Delta x$ is the grid spacing, and $o(\Delta x^2)$ is the truncation error. The latter is introduced when approximating the flow derivatives using a differentiation scheme, which is usually obtained by performing Taylor's expansion of the velocity field until a finite order. The central differencing scheme is second-order accurate; hence the truncation error is of the

order of $\Delta x^2$. This error affects both experimental and simulation data. Since the velocity fields are sampled with a resolution of 0.005 and 0.007 m for the numerical and experimental data, respectively, the truncation error is of the order of $10^{-5}$ and can be considered negligible.

However, for experimental data the calculation of the flow derivatives may also amplify measurement errors that affect the velocity fields obtained with PIV. For this reason, the uncertainty in the vorticity calculation needs to be estimated. For example, following the approach proposed by Sciacchitano and Wieneke (2016), the uncertainty in the vorticity is estimated as

$$ U_{\omega} = \frac{U}{\Delta x} \sqrt{1 - \rho}, \quad (B2) $$

where $U_{\omega}$ and $U$ are the uncertainties in the vorticity and velocity values, respectively, and $\rho$ is the normalized cross-correlation of the measurement error between velocity values at a distance of two grid points. For the PIV measurements
## Appendix A: Characterization of wind tunnel turbulence

During the experimental campaign the inflow conditions of the wind tunnel were investigated (Fig. A1). Due to the presence of the wind tunnel walls, it was not possible to achieve a perfectly uniform wind speed. However, the velocity was almost constant from about 0.5 m above the wind tunnel floor. The turbulence intensity at the wind tunnel inlet was about 2% above 0.5 m; however values up to 10% are measured near to the ground. The integral length scale in the along-wind direction was about 0.2 m and was almost constant along the wind tunnel height.

<figure><img src="image_20.png" /><figcaption>Figure A1. Characterization of wind tunnel inflow with uncertainty range. (a) Vertical velocity profile normalized by wind speed at hub height, (b) turbulence intensity, and (c) integral length scale.</figcaption></figure>

## Appendix B: Uncertainty in vorticity distribution and tip vortex circulation

The vorticity calculation requires the spatial derivatives of the velocity field. Because both numerical and experimental data are obtained over a discrete grid, a differentiation scheme is required. For example, considering a central differencing scheme, the velocity derivative at a grid point (i, j) along the x direction is calculated as

$$ \frac{\partial f}{\partial x}(i, j) = \frac{f(i+1, j) - f(i-1, j)}{2\Delta x} + o(\Delta x^2), \quad (B1) $$

where $\Delta x$ is the grid spacing, and $o(\Delta x^2)$ is the truncation error. The latter is introduced when approximating the flow derivatives using a differentiation scheme, which is usually obtained by performing Taylor's expansion of the velocity field until a finite order. The central differencing scheme is second-order accurate; hence the truncation error is of the

order of $\Delta x^2$. This error affects both experimental and simulation data. Since the velocity fields are sampled with a resolution of 0.005 and 0.007 m for the numerical and experimental data, respectively, the truncation error is of the order of $10^{-5}$ and can be considered negligible.

However, for experimental data the calculation of the flow derivatives may also amplify measurement errors that affect the velocity fields obtained with PIV. For this reason, the uncertainty in the vorticity calculation needs to be estimated. For example, following the approach proposed by Sciacchitano and Wieneke (2016), the uncertainty in the vorticity is estimated as

$$ U_{\omega} = \frac{U}{\Delta x} \sqrt{1 - \rho}, \quad (B2) $$

where $U_{\omega}$ and $U$ are the uncertainties in the vorticity and velocity values, respectively, and $\rho$ is the normalized cross-correlation of the measurement error between velocity values at a distance of two grid points. For the PIV measurements
performed during the experimental campaign, the maximum in-plane velocity error was estimated as 0.07 m s⁻¹, considering a maximum displacement error of 0.1 pixels. Hence, since the spatial resolution of the data was 0.007 m, the maximum uncertainty in the vorticity value is about 10 s⁻¹, assuming ρ = 0. To evaluate the effect of both truncation and measurement errors in the calculation of the tip vortex strength, the circulation results are checked with the same value calculated as the line integral of the velocity field:

$$ \Gamma = \oint \mathbf{u} \cdot d\mathbf{l}. \qquad (B3) $$

The relative error in the tip vortex strength from the two definitions of the circulation is shown in Fig. B1. For both simulations and experiments, the difference between the approaches is less than 1.5%, confirming that estimating the circulation from the vorticity does not introduce significant errors.

<figure><img src="image_21.png" /><figcaption>Figure B1. Relative error in the circulation calculation for both experimental and numerical data. The relative error is estimated by comparing the circulation calculated using Eq. (19) and the value obtained with Eq. (A3). (a) LC 1.1, (b) LC 2.1, (c) LC 2.5, (d) LC 2.7, (e) LC 3.1, (f) LC 3.5, (g) LC 3.7.</figcaption></figure>
performed during the experimental campaign, the maximum in-plane velocity error was estimated as 0.07 m s⁻¹, considering a maximum displacement error of 0.1 pixels. Hence, since the spatial resolution of the data was 0.007 m, the maximum uncertainty in the vorticity value is about 10 s⁻¹, assuming ρ = 0. To evaluate the effect of both truncation and measurement errors in the calculation of the tip vortex strength, the circulation results are checked with the same value calculated as the line integral of the velocity field:

$$ \Gamma = \oint \boldsymbol{u} \cdot d\boldsymbol{l}. \qquad (B3) $$

The relative error in the tip vortex strength from the two definitions of the circulation is shown in Fig. B1. For both simulations and experiments, the difference between the approaches is less than 1.5%, confirming that estimating the circulation from the vorticity does not introduce significant errors.

<figure><img src="image_21.png" /><figcaption>Figure B1. Relative error in the circulation calculation for both experimental and numerical data. The relative error is estimated by comparing the circulation calculated using Eq. (19) and the value obtained with Eq. (A3). (a) LC 1.1, (b) LC 2.1, (c) LC 2.5, (d) LC 2.7, (e) LC 3.1, (f) LC 3.5, (g) LC 3.7.</figcaption></figure>
**Data availability.** The figures shown in Sects. 7.2.1 and 8.1 for LC 2.5 are provided as a Supplement for all the analyzed LCs: https://doi.org/10.5281/zenodo.8210873 (Cioni et al., 2023).

**Competing interests.** At least one of the (co-)authors is a member of the editorial board of *Wind Energy Science*. The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.

**Disclaimer.** The views expressed in the article do not necessarily represent the views of the DOE or the US Government. The US Government retains and the publisher, by accepting the article for publication, acknowledges that the US Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for US Government purposes.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

**Acknowledgements.** The team from Università degli studi di Firenze would like to acknowledge Giovanni Ferrara for the tutoring of Stefano Cioni's PhD and support of this research program. CENER wants to thank the government of Navarre for the funding provided by the Ayudas para la contratación de doctorandos y doctorandas por empresas y organismos de investigación y difusión de conocimientos: doctorados industriales 2019-2021 program that has been used for the development of AeroVIEW.

**Financial support.** DTU's participation in this research has been supported by EUDP (grant no. 64018-0146). TU Delft's contribution was carried out with support from the European Industrial Doctorate program STEP4WIND (H2020-MSCA-ITN-2019, grant agreement 860737) and support from the Dutch Research Council (NWO) through supercomputing time on the Dutch national supercomputer Snellius (grant agreement EINF-20 4659). EDF's participation in this research has been supported by the Association Nationale de la Recherche et de la Technologie (ANRT), CIFRE agreement no. 2018/1790. This work was authored in part by the National Renewable Energy Laboratory, operated by the Alliance for Sustainable Energy, LLC, for the US Department of Energy (DOE) under grant no. DEAC36-08GO28308. Funding was provided by the US Department of Energy's offices of Energy Efficiency and Renewable Energy and Wind Energy Technologies. TUHH was supported by the German Federal Ministry for Economic Affairs and Climate Action (BMWK) through funding the IEA Task and the VAMOS project (03EE2004C), which formed the basis for the presented work.

**Review statement.** This paper was edited by Johan Meyers and reviewed by two anonymous referees.

## References

Arabgolarcheh, A., Jannesarahmadi, S., and Benini, E.: Modeling of near wake characteristics in floating offshore wind turbines using an actuator line method, Renew. Energy, 185, 871–887, https://doi.org/10.1016/j.renene.2021.12.099, 2022.

Bayati, I., Belloli, M., Bernini, L., Boldrin, D. M., Boorsma, K., Caboni, M., Cormier, M., Mikkelsen, R., Lutz, T., and Zasso, A.: UNAFLOW project: UNsteady Aerodynamics of FLOating Wind turbines, J. Phys.: Conf. Ser., 1037, 072037, https://doi.org/10.1088/1742-6596/1037/7/072037, 2018.

Bergua, R., Robertson, A., Jonkman, J., Branlard, E., Fontanella, A., Belloli, M., Schito, P., Zasso, A., Persico, G., Sanvito, A., Amet, E., Brun, C., Campaña-Alonso, G., Martín-San-Román, R., Cai, R., Cai, J., Qian, Q., Maoshi, W., Beardsell, A., Pirrung, G., Ramos-García, N., Shi, W., Fu, J., Corniglion, R., Lovera, A., Galván, J., Nygaard, T. A., dos Santos, C. R., Gilbert, P., Joulin, P.-A., Blondel, F., Frickel, E., Chen, P., Hu, Z., Boisard, R., Yilmazlar, K., Croce, A., Harnois, V., Zhang, L., Li, Y., Aristondo, A., Mendikoa Alonso, I., Mancini, S., Boorsma, K., Savenije, F., Marten, D., Soto-Valle, R., Schulz, C. W., Netzband, S., Bianchini, A., Papi, F., Cioni, S., Trubat, P., Alarcon, D., Molins, C., Cormier, M., Brüker, K., Lutz, T., Xiao, Q., Deng, Z., Haudin, F., and Goveas, A.: OC6 project Phase III: validation of the aerodynamic loading on a wind turbine rotor undergoing large motion caused by a floating support structure, Wind Energ. Sci., 8, 465–485, https://doi.org/10.5194/wes-8-465-2023, 2023.

Boorsma, K., Schepers, J. G., Gomez-Iradi, S., Herraez, I., Lutz, T., Weihing, P., Oggiano, L., Pirrung, G., Madsen, H. A., and Shen, W. Z.: Final report of IEA wind task 29 Mexnext (Phase 3), Report number ECN-E-18-003 ECN Wind Energy, https://publications.ecn.nl/ECN-E-18-003 (last access: 2 November 2023), 2018.

Branlard, E., Brownstein, I., Strom, B., Jonkman, J., Dana, S., and Baring-Gould, E. I.: A multipurpose lifting-line flow solver for arbitrary wind energy concepts, Wind Energ. Sci., 7, 455–467, https://doi.org/10.5194/wes-7-455-2022, 2022.

Butterfield, S., Musial, W., Jonkman, J., and Sclavounos, P.: Engineering Challenges for Floating Offshore Wind Turbines, Report number NREL/CP-500-38776, NREL – National Renewable Energy Lab., Golden, CO, USA, https://www.nrel.gov/docs/fy07osti/38776.pdf (last access: 2 November 2023), 2007.

Chen, J., Hu, Z., Liu, G., and Wan, D.: Coupled aero-hydro-servol-elastic methods for floating wind turbines, Renew. Energy, 130, 139–153, https://doi.org/10.1016/j.renene.2018.06.060, 2019.

Chen, P., Chen, J., and Hu, Z.: Review of Experimental-Numerical Methodologies and Challenges for Floating Offshore Wind Turbines, J. Mar. Sci. Appl., 19, 339–361, https://doi.org/10.1007/s11804-020-00165-z, 2020.

Cioni, S., Papi, F., Pagamonci, L., Bianchini, A., Ramos-García, N., Pirrung, G., Corniglion, R., Lovera, A., Galván, J., Boisard, R., Fontanella, A., Schito, P., Zasso, A., Belloli, M., Sanvito, A., Persico, G., Zhang, L., Li, Y., Zhou, Y., Mancini, S., Boorsma, K., Amaral, R., Viré, A., Schulz, C. W., Netzband, S., Soto-Valle, R., Marten, D., Martín-San-Román, R., Trubat, P.,
**Data availability.** The figures shown in Sects. 7.2.1 and 8.1 for LC 2.5 are provided as a Supplement for all the analyzed LCs: https://doi.org/10.5281/zenodo.8210873 (Cioni et al., 2023).

**Competing interests.** At least one of the (co-)authors is a member of the editorial board of *Wind Energy Science*. The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.

**Disclaimer.** The views expressed in the article do not necessarily represent the views of the DOE or the US Government. The US Government retains and the publisher, by accepting the article for publication, acknowledges that the US Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for US Government purposes.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

**Acknowledgements.** The team from Università degli studi di Firenze would like to acknowledge Giovanni Ferrara for the tutoring of Stefano Cioni's PhD and support of this research program. CENER wants to thank the government of Navarre for the funding provided by the Ayudas para la contratación de doctorandos y doctorandas por empresas y organismos de investigación y difusión de conocimientos: doctorados industriales 2019-2021 program that has been used for the development of AeroVIEW.

**Financial support.** DTU's participation in this research has been supported by EUDP (grant no. 64018-0146). TU Delft's contribution was carried out with support from the European Industrial Doctorate program STEP4WIND (H2020-MSCA-ITN-2019, grant agreement 860737) and support from the Dutch Research Council (NWO) through supercomputing time on the Dutch national supercomputer Snellius (grant agreement EINF-20 4659). EDF's participation in this research has been supported by the Association Nationale de la Recherche et de la Technologie (ANRT), CIFRE agreement no. 2018/1790. This work was authored in part by the National Renewable Energy Laboratory, operated by the Alliance for Sustainable Energy, LLC, for the US Department of Energy (DOE) under grant no. DEAC36-08GO28308. Funding was provided by the US Department of Energy's offices of Energy Efficiency and Renewable Energy and Wind Energy Technologies. TUHH was supported by the German Federal Ministry for Economic Affairs and Climate Action (BMWK) through funding the IEA Task and the VAMOS project (03EE2004C), which formed the basis for the presented work.

**Review statement.** This paper was edited by Johan Meyers and reviewed by two anonymous referees.

## References

Arabgolarcheh, A., Jannesarahmadi, S., and Benini, E.: Modeling of near wake characteristics in floating offshore wind turbines using an actuator line method, Renew. Energy, 185, 871–887, https://doi.org/10.1016/j.renene.2021.12.099, 2022.

Bayati, I., Belloli, M., Bernini, L., Boldrin, D. M., Boorsma, K., Caboni, M., Cormier, M., Mikkelsen, R., Lutz, T., and Zasso, A.: UNAFLOW project: UNsteady Aerodynamics of FLOating Wind turbines, J. Phys.: Conf. Ser., 1037, 072037, https://doi.org/10.1088/1742-6596/1037/7/072037, 2018.

Bergua, R., Robertson, A., Jonkman, J., Branlard, E., Fontanella, A., Belloli, M., Schito, P., Zasso, A., Persico, G., Sanvito, A., Amet, E., Brun, C., Campaña-Alonso, G., Martín-San-Román, R., Cai, R., Cai, J., Qian, Q., Maoshi, W., Beardsell, A., Pirrung, G., Ramos-García, N., Shi, W., Fu, J., Corniglion, R., Lovera, A., Galván, J., Nygaard, T. A., dos Santos, C. R., Gilbert, P., Joulin, P.-A., Blondel, F., Frickel, E., Chen, P., Hu, Z., Boisard, R., Yilmazlar, K., Croce, A., Harnois, V., Zhang, L., Li, Y., Aristondo, A., Mendikoa Alonso, I., Mancini, S., Boorsma, K., Savenije, F., Marten, D., Soto-Valle, R., Schulz, C. W., Netzband, S., Bianchini, A., Papi, F., Cioni, S., Trubat, P., Alarcon, D., Molins, C., Cormier, M., Brüker, K., Lutz, T., Xiao, Q., Deng, Z., Haudin, F., and Goveas, A.: OC6 project Phase III: validation of the aerodynamic loading on a wind turbine rotor undergoing large motion caused by a floating support structure, Wind Energ. Sci., 8, 465–485, https://doi.org/10.5194/wes-8-465-2023, 2023.

Boorsma, K., Schepers, J. G., Gomez-Iradi, S., Herraez, I., Lutz, T., Weihing, P., Oggiano, L., Pirrung, G., Madsen, H. A., and Shen, W. Z.: Final report of IEA wind task 29 Mexnext (Phase 3), Report number ECN-E-18-003 ECN Wind Energy, https://publications.ecn.nl/ECN-E-18-003 (last access: 2 November 2023), 2018.

Branlard, E., Brownstein, I., Strom, B., Jonkman, J., Dana, S., and Baring-Gould, E. I.: A multipurpose lifting-line flow solver for arbitrary wind energy concepts, Wind Energ. Sci., 7, 455–467, https://doi.org/10.5194/wes-7-455-2022, 2022.

Butterfield, S., Musial, W., Jonkman, J., and Sclavounos, P.: Engineering Challenges for Floating Offshore Wind Turbines, Report number NREL/CP-500-38776, NREL – National Renewable Energy Lab., Golden, CO, USA, https://www.nrel.gov/docs/fy07osti/38776.pdf (last access: 2 November 2023), 2007.

Chen, J., Hu, Z., Liu, G., and Wan, D.: Coupled aero-hydro-servo-elastic methods for floating wind turbines, Renew. Energy, 130, 139–153, https://doi.org/10.1016/j.renene.2018.06.060, 2019.

Chen, P., Chen, J., and Hu, Z.: Review of Experimental-Numerical Methodologies and Challenges for Floating Offshore Wind Turbines, J. Mar. Sci. Appl., 19, 339–361, https://doi.org/10.1007/s11804-020-00165-z, 2020.

Cioni, S., Papi, F., Pagamonci, L., Bianchini, A., Ramos-García, N., Pirrung, G., Corniglion, R., Lovera, A., Galván, J., Boisard, R., Fontanella, A., Schito, P., Zasso, A., Belloli, M., Sanvito, A., Persico, G., Zhang, L., Li, Y., Zhou, Y., Mancini, S., Boorsma, K., Amaral, R., Viré, A., Schulz, C. W., Netzband, S., Soto-Valle, R., Marten, D., Martín-San-Román, R., Trubat, P.,
Molins, C., Bergua, R., Branlard, E., Jonkman, J., and Robertson, A.: On the characteristics of the wake of a wind turbine undergoing large motions caused by a floating structure: an insight based on experiments and multi-fidelity simulations from the OC6 Phase III Project – Supplementary material (1.0), Zenodo [data set], https://doi.org/10.5281/zenodo.8210873, 2023.

Cormier, M., Bühler, M., Mauz, M., Lutz, T., Bange, J., and Krämer, E.: CFD Prediction of Tip Vortex Aging in the Wake of a Multi-MW Wind Turbine, J. Phys.: Conf. Ser., 1618, 062029, https://doi.org/10.1088/1742-6596/1618/6/062029, 2020.

Corniglion, R.: Aero-elastic modeling of floating wind turbines with vortex methods, phdthesis, École des Ponts ParisTech, https://pastel.hal.science/tel-03901284 (last access: 2 November 2023), 2022.

Corniglion, R., Harris, J. C., and Peyrard, C.: The aerodynamics of a blade pitch, rotor speed, and surge step for a wind turbine regarding dynamic inflow, Wind Energy, 25, 858–880, https://doi.org/10.1002/we.2702, 2022.

de Vaal, J. B., Hansen, M. O. L., and Moan, T.: Effect of wind turbine surge motion on rotor thrust and induced velocity, Wind Energy, 17, 105–121, https://doi.org/10.1002/we.1562, 2014.

Dong, J. and Viré, A.: The aerodynamics of floating offshore wind turbines in different working states during surge motion, Renew. Energy, 195, 1125–1136, https://doi.org/10.1016/j.renene.2022.06.016, 2022.

Ebert, P. R. and Wood, D. H.: The near wake of a model horizontal-axis wind turbine – II. General features of the three-dimensional flowfield, Renew. Energy, 18, 513–534, https://doi.org/10.1016/S0960-1481(98)00797-6, 1999.

Farrugia, R., Sant, T., and Micallef, D.: A study on the aerodynamics of a floating wind turbine rotor, Renew. Energy, 86, 770–784, https://doi.org/10.1016/j.renene.2015.08.063, 2016.

Ferreira, C., Yu, W., Sala, A., and Viré, A.: Dynamic inflow model for a floating horizontal axis wind turbine in surge motion, Wind Energ. Sci., 7, 469–485, https://doi.org/10.5194/wes-7-469-2022, 2022.

Fontanella, A., Bayati, I., Mikkelsen, R., Belloli, M., and Zasso, A.: UNAFLOW: a holistic wind tunnel experiment about the aerodynamic response of floating wind turbines under imposed surge motion, Wind Energ. Sci., 6, 1169–1190, https://doi.org/10.5194/wes-6-1169-2021, 2021.

Fontanella, A., Facchinetti, A., Di Carlo, S., and Belloli, M.: Wind tunnel investigation of the aerodynamic response of two 15 MW floating wind turbines, Wind Energ. Sci., 7, 1711–1729, https://doi.org/10.5194/wes-7-1711-2022, 2022a.

Fontanella, A., Zasso, A., and Belloli, M.: Wind tunnel investigation of the wake-flow response for a floating turbine subjected to surge motion, J. Phys.: Conf. Ser., 2265, 042023, https://doi.org/10.1088/1742-6596/2265/4/042023, 2022b.

Gao, Z., Feng, X., Zhang, Z., Liu, Z., Gao, X., Zhang, L., Li, S., and Li, Y.: A brief discussion on offshore wind turbine hydrodynamics problem, J. Hydrodynam., 34, 15–30, https://doi.org/10.1007/s42241-022-0002-y, 2022.

Graftieaux, L., Michard, M., and Grosjean, N.: Combining PIV, POD and vortex identification algorithms for the study of unsteady turbulent swirling flows, Meas. Sci. Technol., 12, 1422, https://doi.org/10.1088/0957-0233/12/9/307, 2001.

Inghels, P.: Wind tunnel blockage corrections for wind turbine measurements, Technical report, Royal Institute of

Technology KTH Mechanics, https://kth.diva-portal.org/smash/get/diva2:1078083/FULLTEXT01.pdf (last access: 2 November 2023), 2013.

Johlas, H. M., Martínez-Tossas, L. A., Churchfield, M. J., Lackner, M. A., and Schmidt, D. P.: Floating platform effects on power generation in spar and semisubmersible wind turbines, Wind Energy, 24, 901–916, https://doi.org/10.1002/we.2608, 2021.

Jonkman, J. M. and Matha, D.: Dynamics of offshore floating wind turbines – analysis of three concepts, Wind Energy, 14, 557–569, https://doi.org/10.1002/we.442, 2011.

Kleine, V. G., Franceschini, L., Carmo, B. S., Hanifi, A., and Henningson, D. S.: Stability of Floating Wind Turbine Wakes, J. Phys.: Conf. Ser., 1934, 012009, https://doi.org/10.1088/1742-6596/1934/1/012009, 2021.

Kleine, V. G., Franceschini, L., Carmo, B. S., Hanifi, A., and Henningson, D. S.: The stability of wakes of floating wind turbines, Phys. Fluids, 34, 074106, https://doi.org/10.1063/5.0092267, 2022.

Larsen, G. C., Madsen, H. Aa., Thomsen, K., and Larsen, T. J.: Wake meandering: a pragmatic approach, Wind Energy, 11, 377–395, https://doi.org/10.1002/we.267, 2008.

Larsen, T. J. and Hanson, T. D.: A method to avoid negative damped low frequent tower vibrations for a floating pitch controlled wind turbine, J. Phys.: Conf. Ser., 75, 012073, https://doi.org/10.1088/1742-6596/75/1/012073, 2007.

Leishman, G. J.: Principles of Helicopter Aerodynamics with CD Extra, Cambridge University Press, 860 pp., ISBN 0-521-85860-7, 2006.

Mancini, S., Boorsma, K., Caboni, M., Cormier, M., Lutz, T., Schito, P., and Zasso, A.: Characterization of the unsteady aerodynamic response of a floating offshore wind turbine to surge motion, Wind Energ. Sci., 5, 1713–1730, https://doi.org/10.5194/wes-5-1713-2020, 2020.

Marten, D., Paschereit, C. O., Huang, X., Meinke, M., Schröder, W., Müller, J., and Oberleithner, K.: Predicting Wind Turbine Wake Breakdown Using a Free Vortex Wake Code, AIAA J., 58, 4672–4685, https://doi.org/10.2514/1.J058308, 2020.

Martín-San-Román, R., Benito-Cia, P., Azcona-Armendáriz, J., and Cuerva-Tejero, A.: Validation of a free vortex filament wake module for the integrated simulation of multi-rotor wind turbines, Renew. Energy, 179, 1706–1718, https://doi.org/10.1016/j.renene.2021.07.147, 2021.

Massouh, F. and Dobrev, I.: Investigation of wind turbine flow and wake, J. Fluid Sci. Technol., 9, JFST0025, https://doi.org/10.1299/jfst.2014jfst0025, 2014.

Melani, P. F., Balduzzi, F., and Bianchini, A.: Simulating tip effects in vertical-axis wind turbines with the actuator line method, J. Phys.: Conf. Ser., 2265, 032028, https://doi.org/10.1088/1742-6596/2265/3/032028, 2022.

Netzband, S., Schulz, C. W., Götsche, U., Ferreira González, D., and Abdel-Maksoud, M.: A panel method for floating offshore wind turbine simulations with fully integrated aero- and hydrodynamic modelling in time domain, Ship Technol. Res., 65, 123–136, https://doi.org/10.1080/09377255.2018.1475710, 2018.

Odemark, Y. and Fransson, J. H. M.: The stability and development of tip and root vortices behind a model wind turbine, Exp. Fluids, 54, 1591, https://doi.org/10.1007/s00348-013-1591-6, 2013.

Okulov, V. L. and Sørensen, J. N.: Maximum efficiency of wind turbine rotors using Joukowsky and
Molins, C., Bergua, R., Branlard, E., Jonkman, J., and Robertson, A.: On the characteristics of the wake of a wind turbine undergoing large motions caused by a floating structure: an insight based on experiments and multi-fidelity simulations from the OC6 Phase III Project – Supplementary material (1.0), Zenodo [data set], https://doi.org/10.5281/zenodo.8210873, 2023.

Cormier, M., Bühler, M., Mauz, M., Lutz, T., Bange, J., and Krämer, E.: CFD Prediction of Tip Vortex Aging in the Wake of a Multi-MW Wind Turbine, J. Phys.: Conf. Ser., 1618, 062029, https://doi.org/10.1088/1742-6596/1618/6/062029, 2020.

Corniglion, R.: Aero-elastic modeling of floating wind turbines with vortex methods, phdthesis, École des Ponts ParisTech, https://pastel.hal.science/tel-03901284 (last access: 2 November 2023), 2022.

Corniglion, R., Harris, J. C., and Peyrard, C.: The aerodynamics of a blade pitch, rotor speed, and surge step for a wind turbine regarding dynamic inflow, Wind Energy, 25, 858–880, https://doi.org/10.1002/we.2702, 2022.

de Vaal, J. B., Hansen, M. O. L., and Moan, T.: Effect of wind turbine surge motion on rotor thrust and induced velocity, Wind Energy, 17, 105–121, https://doi.org/10.1002/we.1562, 2014.

Dong, J. and Viré, A.: The aerodynamics of floating offshore wind turbines in different working states during surge motion, Renew. Energy, 195, 1125–1136, https://doi.org/10.1016/j.renene.2022.06.016, 2022.

Ebert, P. R. and Wood, D. H.: The near wake of a model horizontal-axis wind turbine – II. General features of the three-dimensional flowfield, Renew. Energy, 18, 513–534, https://doi.org/10.1016/S0960-1481(98)00797-6, 1999.

Farrugia, R., Sant, T., and Micallef, D.: A study on the aerodynamics of a floating wind turbine rotor, Renew. Energy, 86, 770–784, https://doi.org/10.1016/j.renene.2015.08.063, 2016.

Ferreira, C., Yu, W., Sala, A., and Viré, A.: Dynamic inflow model for a floating horizontal axis wind turbine in surge motion, Wind Energ. Sci., 7, 469–485, https://doi.org/10.5194/wes-7-469-2022, 2022.

Fontanella, A., Bayati, I., Mikkelsen, R., Belloli, M., and Zasso, A.: UNAFLOW: a holistic wind tunnel experiment about the aerodynamic response of floating wind turbines under imposed surge motion, Wind Energ. Sci., 6, 1169–1190, https://doi.org/10.5194/wes-6-1169-2021, 2021.

Fontanella, A., Facchinetti, A., Di Carlo, S., and Belloli, M.: Wind tunnel investigation of the aerodynamic response of two 15 MW floating wind turbines, Wind Energ. Sci., 7, 1711–1729, https://doi.org/10.5194/wes-7-1711-2022, 2022a.

Fontanella, A., Zasso, A., and Belloli, M.: Wind tunnel investigation of the wake-flow response for a floating turbine subjected to surge motion, J. Phys.: Conf. Ser., 2265, 042023, https://doi.org/10.1088/1742-6596/2265/4/042023, 2022b.

Gao, Z., Feng, X., Zhang, Z., Liu, Z., Gao, X., Zhang, L., Li, S., and Li, Y.: A brief discussion on offshore wind turbine hydrodynamics problem, J. Hydrodynam., 34, 15–30, https://doi.org/10.1007/s42241-022-0002-y, 2022.

Graftieaux, L., Michard, M., and Grosjean, N.: Combining PIV, POD and vortex identification algorithms for the study of unsteady turbulent swirling flows, Meas. Sci. Technol., 12, 1422, https://doi.org/10.1088/0957-0233/12/9/307, 2001.

Inghels, P.: Wind tunnel blockage corrections for wind turbine measurements, Technical report, Royal Institute of

Technology KTH Mechanics, https://kth.diva-portal.org/smash/get/diva2:1078083/FULLTEXT01.pdf (last access: 2 November 2023), 2023.

Johlas, H. M., Martínez-Tossas, L. A., Churchfield, M. J., Lackner, M. A., and Schmidt, D. P.: Floating platform effects on power generation in spar and semisubmersible wind turbines, Wind Energy, 24, 901–916, https://doi.org/10.1002/we.2608, 2021.

Jonkman, J. M. and Matha, D.: Dynamics of offshore floating wind turbines – analysis of three concepts, Wind Energy, 14, 557–569, https://doi.org/10.1002/we.442, 2011.

Kleine, V. G., Franceschini, L., Carmo, B. S., Hanifi, A., and Henningson, D. S.: Stability of Floating Wind Turbine Wakes, J. Phys.: Conf. Ser., 1934, 012009, https://doi.org/10.1088/1742-6596/1934/1/012009, 2021.

Kleine, V. G., Franceschini, L., Carmo, B. S., Hanifi, A., and Henningson, D. S.: The stability of wakes of floating wind turbines, Phys. Fluids, 34, 074106, https://doi.org/10.1063/5.0092267, 2022.

Larsen, G. C., Madsen, H. Aa., Thomsen, K., and Larsen, T. J.: Wake meandering: a pragmatic approach, Wind Energy, 11, 377–395, https://doi.org/10.1002/we.267, 2008.

Larsen, T. J. and Hanson, T. D.: A method to avoid negative damped low frequent tower vibrations for a floating pitch controlled wind turbine, J. Phys.: Conf. Ser., 75, 012073, https://doi.org/10.1088/1742-6596/75/1/012073, 2007.

Leishman, G. J.: Principles of Helicopter Aerodynamics with CD Extra, Cambridge University Press, 860 pp., ISBN 0-521-85860-7, 2006.

Mancini, S., Boorsma, K., Caboni, M., Cormier, M., Lutz, T., Schito, P., and Zasso, A.: Characterization of the unsteady aerodynamic response of a floating offshore wind turbine to surge motion, Wind Energ. Sci., 5, 1713–1730, https://doi.org/10.5194/wes-5-1713-2020, 2020.

Marten, D., Paschereit, C. O., Huang, X., Meinke, M., Schröder, W., Müller, J., and Oberleithner, K.: Predicting Wind Turbine Wake Breakdown Using a Free Vortex Wake Code, AIAA J., 58, 4672–4685, https://doi.org/10.2514/1.J058308, 2020.

Martín-San-Román, R., Benito-Cia, P., Azcona-Armendáriz, J., and Cuerva-Tejero, A.: Validation of a free vortex filament wake module for the integrated simulation of multi-rotor wind turbines, Renew. Energy, 179, 1706–1718, https://doi.org/10.1016/j.renene.2021.07.147, 2021.

Massouh, F. and Dobrev, I.: Investigation of wind turbine flow and wake, J. Fluid Sci. Technol., 9, JFST0025, https://doi.org/10.1299/jfst.2014jfst0025, 2014.

Melani, P. F., Balduzzi, F., and Bianchini, A.: Simulating tip effects in vertical-axis wind turbines with the actuator line method, J. Phys.: Conf. Ser., 2265, 032028, https://doi.org/10.1088/1742-6596/2265/3/032028, 2022.

Netzband, S., Schulz, C. W., Götsche, U., Ferreira González, D., and Abdel-Maksoud, M.: A panel method for floating offshore wind turbine simulations with fully integrated aero- and hydrodynamic modelling in time domain, Ship Technol. Res., 65, 123–136, https://doi.org/10.1080/09377255.2018.1475710, 2018.

Odemark, Y. and Fransson, J. H. M.: The stability and development of tip and root vortices behind a model wind turbine, Exp. Fluids, 54, 1591, https://doi.org/10.1007/s00348-013-1591-6, 2013.

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Ostovan, Y., Akpolat, M. T., and Uzol, O.: Experimental Investigation of the Effects of Winglets on the Tip Vortex Behavior of a Model Horizontal Axis Wind Turbine Using Particle Image Velocimetry, J. Sol. Energ. Eng., 141, SOL-17-1391, https://doi.org/10.1115/1.4041154, 2018.

Pirrung, G. R. and Madsen, H. A.: Dynamic inflow effects in measurements and high-fidelity computations, Wind Energ. Sci., 3, 545–551, https://doi.org/10.5194/wes-3-545-2018, 2018.

Ramos-García, N., Sessarego, M., and Horcas, S. G.: Aero-hydro-servo-elastic coupling of a multi-body finite-element solver and a multi-fidelity vortex method, Wind Energy, 24, 481–501, https://doi.org/10.1002/we.2584, 2021.

Ramos-García, N., Kontos, S., Pegalajar-Jurado, A., González Horcas, S., and Bredmose, H.: Investigation of the floating IEA Wind 15 MW RWT using vortex methods Part I: Flow regimes and wake recovery, Wind Energy, 25, 468–504, https://doi.org/10.1002/we.2682, 2022.

Robertson, A., Bergua, R., Fontanella, A., and Jonkman, J.: OC6 Phase III Definition Document: Validation of Nonlinear Hydrodynamic Loading on the DeepCwind Semisubmersible, Technical report NREL/TP-5000-80803, NREL, https://www.nrel.gov/docs/fy22osti/80803.pdf (last access: 2 November 2023), 2023.

Saverin, J., Perez-Becker, S., Behrens De Luna, R., Marten, D., Gilloteaux, J.-C., and Kurnia, R.: D1.2 Higher Order Hydroelastic Module, Zenodo, https://doi.org/10.5281/zenodo.6958081, 2021.

Sciacchitano, A. and Wieneke, B.: PIV uncertainty propagation, Meas. Sci. Technol., 27, 084006, https://doi.org/10.1088/0957-0233/27/8/084006, 2016.

Sebastian, T. and Lackner, M. A.: Characterization of the unsteady aerodynamics of offshore floating wind turbines, Wind Energy, 16, 339–352, https://doi.org/10.1002/we.545, 2013.

Shaler, K., Branlard, E., and Platt, A.: OLAF User's Guide and Theory Manual, OSTI.GOV, https://doi.org/10.2172/1659853, 2020.

Shives, M. and Crawford, C.: Mesh and load distribution requirements for actuator line CFD simulations, Wind Energy, 16, 1183–1196, https://doi.org/10.1002/we.1546, 2013.

Snel, H. and Schepers, J.: Investigation and modelling of dynamic inflow effects, Report number ECN-RX-93-029, ECN, https://www.osti.gov/etdeweb/biblio/6413317 (last access: 2 November 2023), 1993.

Snel, H., Schepers, J. G., and Montgomerie, B.: The MEXICO project (Model Experiments in Controlled Conditions): The database and first results of data processing and interpretation, J. Phys.: Conf. Ser., 75, 012014, https://doi.org/10.1088/1742-6596/75/1/012014, 2007.

Soto-Valle, R., Alber, J., Manolesos, M., Nayeri, C. N., and Paschereit, C. O.: Wind Turbine Tip Vortices under the influence of Wind Tunnel Blockage Effects, J. Phys.: Conf. Ser., 1618, 032045, https://doi.org/10.1088/1742-6596/1618/3/032045, 2020.

Soto-Valle, R., Cioni, S., Bartholomay, S., Manolesos, M., Nayeri, C. N., Bianchini, A., and Paschereit, C. O.: Vortex identification methods applied to wind turbine tip vortices, Wind Energ. Sci., 7, 585–602, https://doi.org/10.5194/wes-7-585-2022, 2022.

Theodorsen, T.: General Theory of Aerodynamic Instability and the Mechanism of Flutter, Report number NACA-TR-496, NASA, https://ntrs.nasa.gov/citations/19930090935 (last access: 2 November 2023), 1949.

Tran, T.-T. and Kim, D.-H.: The platform pitching motion of floating offshore wind turbine: A preliminary unsteady aerodynamic analysis, J. Wind Eng. Indust. Aerodynam., 142, 65–81, https://doi.org/10.1016/j.jweia.2015.03.009, 2015.

Tran, T. T. and Kim, D.-H.: A CFD study into the influence of unsteady aerodynamic interference on wind turbine surge motion, Renew. Energy, 90, 204–228, https://doi.org/10.1016/j.renene.2015.12.013, 2016.

van der Wall, B. G. and Richard, H.: Analysis methodology for 3C-PIV data of rotary wing vortices, Exp. Fluids, 40, 798–812, https://doi.org/10.1007/s00348-006-0117-x, 2006.

Vanelli, T., Rinker, J., and Zalkind, D. S.: Aeroservoelastic stability of a floating wind turbine, J. Phys.: Conf. Ser., 2265, 042001, https://doi.org/10.1088/1742-6596/2265/4/042001, 2022.

Van Garrel, A.: Development of a wind turbine aerodynamics simulation module, Report number ECN-C-03-079, https://www.osti.gov/etdeweb/biblio/20405682 (last access: 2 November 2023), 2003.

Veers, P., Bottasso, C., Manuel, L., Naughton, J., Pao, L., Paquette, J., Robertson, A., Robinson, M., Ananthan, S., Barlas, A., Bianchini, A., Bredmose, H., Horcas, S. G., Keller, J., Madsen, H. A., Manwell, J., Moriarty, P., Nolet, S., and Rinker, J.: Grand Challenges in the Design, Manufacture, and Operation of Future Wind Turbine Systems, Wind Energ. Sci., 8, 1071–1131, https://doi.org/10.5194/wes-8-1071-2023, 2023.

Wang, Q., Liao, K., and Ma, Q.: The Influence of Tilt Angle on the Aerodynamic Performance of a Wind Turbine, Appl. Sci., 10, 5380, https://doi.org/10.3390/app10155380, 2020.

Wang, Y. and Abdel-Maksoud, M.: Coupling wake alignment lifting line method and boundary element method for open water and unsteady propeller simulation, Ocean Eng., 213, 107738, https://doi.org/10.1016/j.oceaneng.2020.107738, 2020.

Wei, N. J. and Dabiri, J. O.: Phase-Averaged Dynamics of a Periodically Surging Wind Turbine, J. Renew. Sustain. Energ., 14, 013305, https://doi.org/10.1063/5.0076029, 2022.

Yang, X. and Sotiropoulos, F.: A Review on the Meandering of Wind Turbine Wakes, Energies, 12, 4725, https://doi.org/10.3390/en12244725, 2019.

Yang, Z., Sarkar, P., and Hu, H.: Visualization of the tip vortices in a wind turbine wake, J. Visual., 15, 39–44, https://doi.org/10.1007/s12650-011-0112-z, 2012.
Betz approaches, J. Fluid Mech., 649, 497–508, https://doi.org/10.1017/S0022112010000509, 2010.

Ostovan, Y., Akpolat, M. T., and Uzol, O.: Experimental Investigation of the Effects of Winglets on the Tip Vortex Behavior of a Model Horizontal Axis Wind Turbine Using Particle Image Velocimetry, J. Sol. Energ. Eng., 141, SOL-17-1391, https://doi.org/10.1115/1.4041154, 2018.

Pirrung, G. R. and Madsen, H. A.: Dynamic inflow effects in measurements and high-fidelity computations, Wind Energ. Sci., 3, 545–551, https://doi.org/10.5194/wes-3-545-2018, 2018.

Ramos-García, N., Sessarego, M., and Horcas, S. G.: Aero-hydro-servo-elastic coupling of a multi-body finite-element solver and a multi-fidelity vortex method, Wind Energy, 24, 481–501, https://doi.org/10.1002/we.2584, 2021.

Ramos-García, N., Kontos, S., Pegalajar-Jurado, A., González Horcas, S., and Bredmose, H.: Investigation of the floating IEA Wind 15 MW RWT using vortex methods Part I: Flow regimes and wake recovery, Wind Energy, 25, 468–504, https://doi.org/10.1002/we.2682, 2022.

Robertson, A., Bergua, R., Fontanella, A., and Jonkman, J.: OC6 Phase III Definition Document: Validation of Nonlinear Hydrodynamic Loading on the DeepCwind Semisubmersible, Technical report NREL/TP-5000-80803, NREL, https://www.nrel.gov/docs/fy22osti/80803.pdf (last access: 2 November 2023), 2023.

Saverin, J., Perez-Becker, S., Behrens De Luna, R., Marten, D., Gilloteaux, J.-C., and Kurnia, R.: D1.2 Higher Order Hydroelastic Module, Zenodo, https://doi.org/10.5281/zenodo.6958081, 2021.

Sciacchitano, A. and Wieneke, B.: PIV uncertainty propagation, Meas. Sci. Technol., 27, 084006, https://doi.org/10.1088/0957-0233/27/8/084006, 2016.

Sebastian, T. and Lackner, M. A.: Characterization of the unsteady aerodynamics of offshore floating wind turbines, Wind Energy, 16, 339–352, https://doi.org/10.1002/we.545, 2013.

Shaler, K., Branlard, E., and Platt, A.: OLAF User's Guide and Theory Manual, OSTI.GOV, https://doi.org/10.2172/1659853, 2020.

Shives, M. and Crawford, C.: Mesh and load distribution requirements for actuator line CFD simulations, Wind Energy, 16, 1183–1196, https://doi.org/10.1002/we.1546, 2013.

Snel, H. and Schepers, J.: Investigation and modelling of dynamic inflow effects, Report number ECN-RX-93-029, ECN, https://www.osti.gov/etdeweb/biblio/6413317 (last access: 2 November 2023), 1993.

Snel, H., Schepers, J. G., and Montgomerie, B.: The MEXICO project (Model Experiments in Controlled Conditions): The database and first results of data processing and interpretation, J. Phys.: Conf. Ser., 75, 012014, https://doi.org/10.1088/1742-6596/75/1/012014, 2007.

Soto-Valle, R., Alber, J., Manolesos, M., Nayeri, C. N., and Paschereit, C. O.: Wind Turbine Tip Vortices under the influence of Wind Tunnel Blockage Effects, J. Phys.: Conf. Ser., 1618, 032045, https://doi.org/10.1088/1742-6596/1618/3/032045, 2020.

Soto-Valle, R., Cioni, S., Bartholomay, S., Manolesos, M., Nayeri, C. N., Bianchini, A., and Paschereit, C. O.: Vortex identification methods applied to wind turbine tip vortices, Wind Energ. Sci., 7, 585–602, https://doi.org/10.5194/wes-7-585-2022, 2022.

Theodorsen, T.: General Theory of Aerodynamic Instability and the Mechanism of Flutter, Report number NACA-TR-496, NASA, https://ntrs.nasa.gov/citations/19930090935 (last access: 2 November 2023), 1949.

Tran, T.-T. and Kim, D.-H.: The platform pitching motion of floating offshore wind turbine: A preliminary unsteady aerodynamic analysis, J. Wind Eng. Indust. Aerodynam., 142, 65–81, https://doi.org/10.1016/j.jweia.2015.03.009, 2015.

Tran, T. T. and Kim, D.-H.: A CFD study into the influence of unsteady aerodynamic interference on wind turbine surge motion, Renew. Energy, 90, 204–228, https://doi.org/10.1016/j.renene.2015.12.013, 2016.

van der Wall, B. G. and Richard, H.: Analysis methodology for 3C-PIV data of rotary wing vortices, Exp. Fluids, 40, 798–812, https://doi.org/10.1007/s00348-006-0117-x, 2006.

Vanelli, T., Rinker, J., and Zalkind, D. S.: Aeroservoelastic stability of a floating wind turbine, J. Phys.: Conf. Ser., 2265, 042001, https://doi.org/10.1088/1742-6596/2265/4/042001, 2022.

Van Garrel, A.: Development of a wind turbine aerodynamics simulation module, Report number ECN-C-03-079, https://www.osti.gov/etdeweb/biblio/20405682 (last access: 2 November 2023), 2003.

Veers, P., Bottasso, C., Manuel, L., Naughton, J., Pao, L., Paquette, J., Robertson, A., Robinson, M., Ananthan, S., Barlas, A., Bianchini, A., Bredmose, H., Horcas, S. G., Keller, J., Madsen, H. A., Manwell, J., Moriarty, P., Nolet, S., and Rinker, J.: Grand Challenges in the Design, Manufacture, and Operation of Future Wind Turbine Systems, Wind Energ. Sci., 8, 1071–1131, https://doi.org/10.5194/wes-8-1071-2023, 2023.

Wang, Q., Liao, K., and Ma, Q.: The Influence of Tilt Angle on the Aerodynamic Performance of a Wind Turbine, Appl. Sci., 10, 5380, https://doi.org/10.3390/app10155380, 2020.

Wang, Y. and Abdel-Maksoud, M.: Coupling wake alignment lifting line method and boundary element method for open water and unsteady propeller simulation, Ocean Eng., 213, 107738, https://doi.org/10.1016/j.oceaneng.2020.107738, 2020.

Wei, N. J. and Dabiri, J. O.: Phase-Averaged Dynamics of a Periodically Surging Wind Turbine, J. Renew. Sustain. Energ., 14, 013305, https://doi.org/10.1063/5.0076029, 2022.

Yang, X. and Sotiropoulos, F.: A Review on the Meandering of Wind Turbine Wakes, Energies, 12, 4725, https://doi.org/10.3390/en12244725, 2019.

Yang, Z., Sarkar, P., and Hu, H.: Visualization of the tip vortices in a wind turbine wake, J. Visual., 15, 39–44, https://doi.org/10.1007/s12650-011-0112-z, 2012.