the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 09 Sep 2026
Experimental evidence of wake-rotor synchronization and its effects on the aerodynamic response of tandem floating wind turbines
Abstract. Platform motions of floating wind turbines generate periodic velocity fluctuations in the wake, but how these fluctuations synchronize with the motion of downstream rotors and modify their aerodynamic response remains poorly understood. In particular, experimental evidence of this wake–rotor coupling between multiple moving floating turbines is still lacking. A controlled wind-tunnel experiment was designed to isolate this mechanism using two 1:150 scale DTU 10 MW turbines arranged in tandem and subjected to prescribed harmonic surge motions. Motion reduced frequency (0.12–0.48) and the relative phase between the upstream and downstream turbine motions were systematically varied, while configurations with only one turbine moving were used to separate wake-induced and motion-induced contributions. Aerodynamic loads, equivalent aerodynamic damping, wake velocity fields, and farm-level power were analyzed. The upstream turbine motion generates coherent wake-velocity oscillations synchronized with the imposed surge, and the amplitude of velocity oscillations depends strongly on motion reduced frequency. When this periodically modulated wake interacts with the moving downstream rotor, its aerodynamic response becomes strongly dependent on the relative phase between the two turbine motions. In-phase motion produces the largest oscillations of downstream turbine thrust and the largest equivalent aerodynamic damping, whereas anti-phase motion reduces the amplitude of thrust oscillations and the damping to approximately half that of the upstream turbine. Across the investigated conditions, wake interaction systematically reduces the aerodynamic damping of the downstream turbine relative to the upstream turbine. In parallel, at the higher reduced frequency of 0.48, coherent wake pulsations also enhance wake recovery and increase power of the downstream turbine, whereas these effects are weaker at the lower reduced frequency of 0.12. These results provide experimental evidence that wake coupling between moving floating turbines is a phase-dependent interaction that affects aerodynamic loads, energy capture downstream in the farm and also the effective aerodynamic damping governing floating-turbine response.
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Status: final response (author comments only)
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RC1: 'Comment on wes-2026-151', Anonymous Referee #1, 22 Sep 2026
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AC1: 'Reply on RC1', Alessandro Fontanella, 25 Sep 2026
Dear Referee, thank you for taking the time to revise our article carefully and in a short time. We really appreciate it. Since the Discussion window has been extended until October 18th, we would like to make use of the additional time to continue the discussion with you reporting here some hot takes on your comments. We would be pleased to hear your opinion on our proposed answers so we can better address the comments during the revision stage.
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General comment: In particular, I would suggest the authors include more relevant literature to clearly identify the existing body of knowledge, gaps, and their own novelty (especially since many results were reported by previous studies).
Answer: We propose to revise the introduction, in particular the text from lines 130 to 138, to clarify the specific contribution of this article compared with the existing literature. We reported several studies examining the wakes of floating wind turbines by means of wind tunnel experiments, full-scale measurements, and CFD. Among the many articles that have flourished in recent years, we selected those that appear to have sound methodologies and results and whose authors are known in the research community for their contributions to this field. We also covered studies of wake interactions between different floating turbines (i.e., all turbines with platform motions), which have so far been investigated using CFD only. Please let us know if we have overlooked any relevant previous studies, and we will be happy to examine them.
In reason for the literature we examined, the specific contribution and main novelty of this work is the experimental identification and quantification of aerodynamic coupling between the periodically modulated wake of an upstream turbine and a moving downstream rotor. Beyond characterizing the wake perturbations generated by upstream turbine motion the present work examines how downstream turbine motion reinforces or counteracts their effects on rotor loads. To isolate this interaction, the experiment combines test configurations in which either turbine moves independently with configurations in which both turbines move at prescribed relative phases. The resulting measurements – published as an open-access dataset – characterize this wake–rotor synchronization under controlled conditions, providing a basis for assessing its relevance to floating wind-farm dynamics and for validating numerical simulation tools in this regard.
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1. It seems that the lowest tip-swept point/clearance of the turbine model is only 6.9 cm from the platform; any evaluation of this effect?
We acknowledge the limited blade-tip-to-platform clearance as a limitation of the present experimental setup (it is about 1/3 of the scaled distance from blade tip to sea level in a full-scale floating turbine). Although we do not expect it to significantly affect the main findings of the study, we cannot completely rule out some influence on the measured aerodynamic response.
Nevertheless, the upstream turbine load response and its wake behavior discussed in the manuscript are consistent with those reported in other recent studies – experimental and numerical – using different setups.
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2. Lines 160-165: Maybe explain or cite a reference regarding the rotor design and where this analysis was made.
The rotor design process is explained in the reference “Fontanella et al., 2023” mentioned in line 158. Please let us know if the content of the reference addresses your point and if you would like the reference to be moved to another point in the text.
Fontanella, A., Da Pra, G., and Belloli, M.: Integrated Design and Experimental Validation of a Fixed-Pitch Rotor for Wind Tunnel Testing, Energies, 16, https://doi.org/10.3390/en16052205, 2023.
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3. Lines 168-169: Please specify the dynamic parameters for the motion platform/motor, or cite relevant references.
The dynamic parameters of the motion platform are reported in the reference “Fontanella et al., 2024” mentioned in line 167. Please let us know if the content of the reference addresses your point and if you would like the reference to be moved to another point in the text.
Fontanella, A., Palombini, G., Piffer, A., Giberti, H., and Belloli, M.: Design of a robotic platform for hybrid wind tunnel experiments of floating wind farms, Journal of Physics: Conference Series, 2767, 042 008, https://doi.org/10.1088/1742-6596/2767/4/042008, 2024.
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4. Why was an inflow with no-shear and 2% turbulence intensity used? For the reason of revealing pure motion effects, shouldn’t it be more appropriate to use laminar flow?
We agree that an ideally uniform, turbulence-free inflow would provide a cleaner reference for isolating the effects of platform motion. However, such conditions were not achievable in the large wind-tunnel test section used for these experiments, where a residual background turbulence intensity of approximately 2% is normally present. The larger test section allowed us to use larger rotors compared with other facilities that can achieve lower turbulence levels, but at the cost of using smaller wind turbines, with associated issues (lower Reynolds number, reduced geometric accuracy of small blades, lower magnitude of the loads to be measured, and difficulty in fitting sensors into the model).
The uniform mean inflow was therefore selected to minimize additional inflow effects within the facility’s practical capabilities. Furthermore, the fixed-base and prescribed-motion cases were tested under the same background inflow conditions, allowing the effects of platform motion to be assessed relative to a consistent baseline.
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5. Line 176: Any evidence or reference that shows the profiles of velocity and turbulence intensity? Seems it is quite close to the ground that part of the model would be immersed in the wall boundary layer.
Thank you for raising this point. Indeed, reporting measurements of the undisturbed inflow over the test section in the vertical direction is a valuable addition, and we would include this information in the appendix of the article.
Figure A1 reports the vertical profiles of mean streamwise velocity and turbulence intensity in the wind-tunnel test section at the location of the upstream wind turbine, measured without the turbine. The inflow in the test section was characterized prior to the experiments by measuring profiles of streamwise velocity along vertical lines at lateral distances of y = [-0.25, 0, 0.5, 0.75] m. The spatial average of the mean streamwise velocity shows deviations ranging from -3% to +1% relative to the reference wind speed U0 between the upper and lower rotor edges. For a fixed z position, there are min/max variations of approximately ±5% compared with the mean value. The mean wind speed decreases towards the floor, but the variations within the rotor area are small and comparable to the min/max variations in the lateral direction.
The turbulence intensity in the upper half of the rotor is between 1% and 2%. In the lower half of the rotor, it rises to approximately 3.5% on average for a given height, with larger min/max variations in the lateral direction compared with those at greater distances from the ground.
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6. Lines 197-198: I would expect evidence or references regarding this. And how would fixed rotor speeds make the results differ from varying ones? Which scheme is more likely to be used in reality?
If by “this” you mean “since no significant changes in the mean wake velocity were observed between the fixed and motion cases,” evidence is provided in Fig. 4a. We can make a stronger connection to this result in Sect. 2.2.2 by anticipating it there.
Since the mean wind speed experienced by the downstream rotor does not change when the upstream turbine undergoes surge motion compared with when it is fixed, there is no need to use different rotor-speed regulations to achieve the same TSR. Full-scale commercial turbines regulate the steady-state rotor speed to maintain the TSR close to its optimal value following slow variations in wind speed. This would be the same as in this experiment, where we matched the target TSR based on the mean wind speed.
Full-scale turbines also experience dynamic variations in rotor speed depending on how effectively they track the rotor-speed set point in the presence of wind fluctuations. This is not done in the experiment, where the rotor speed is fixed. The reasons for this are: 1) the control strategy of a full-scale turbine cannot be directly transferred 1:1 to a model-scale turbine and doing so introduces unavoidable differences anyway [1]; 2) introducing a time-varying rotor speed together with platform motion further complicates the rotor aerodynamic response and increases its uncertainty [2].
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7. Lines 232-234: “At full scale…” References should be provided to support the ranges of motion frequencies.
The full scale frequencies of some examples of floating platforms for 10 MW turbines are reported in the references reported in lines 230-232: “The specific frequency values were chosen based on four floating wind turbine concepts designed for the DTU 10 MW reference turbine: the SWE TripleSpar (Lemmer et al., 2020), the LIFES50+ Nautilus (Wise and Bachynski, 2020), the NTNU 10-MW spar (Wise and Bachynski, 2020), and the Softwind spar (Arnal, 2020)”. Let us know if the content of the references address your point and if you would like to have the references moved in another point of the text.
Lemmer, F., Raach, S., Schlipf, D., Faerron-Guzmán, R., and Cheng, P. W.: FAST model of the SWE-TripleSpar floating wind turbine platform for the DTU 10MW reference wind turbine, https://doi.org/10.18419/DARUS-514, 2020.
Wise, A. S. and Bachynski, E. E.: Wake meandering effects on floating wind turbines, Wind Energy, 23, 1266–1285, https://doi.org/https://doi.org/10.1002/we.2485, 2020.
Arnal, V.: Experimental modelling of a floating wind turbine using a “software-in-the-loop” approach, Theses, École centrale de Nantes, https://theses.hal.science/tel-03237441, 2020.
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8. Lines 247-248: “…, while aerodynamics… scale linearly…” Why does aerodynamic force scale linearly with frequency? Is it applicable to all ranges of frequencies (or St)?
Thank you for this comment. Indeed, this statement needs to be better substantiated. It has been shown experimentally and using several aerodynamic simulation tools [2] (see, for example, Fig. 17) that the oscillations of aerodynamic loads are linearly proportional to the motion frequency for reduced frequencies (St) up to ~1.1, which covers those included in the present experiment. This is because, for relatively slow motions, the rotor aerodynamic response is driven by the apparent wind speed created by the motion (see explanation in lines 254–258). For higher motion frequencies, the linear proportionality of load oscillations to motion frequency may no longer hold, with increases or decreases relative to the linear trend depending on the rotor design [3].
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9. Lines 250-251: “Previous…negligible.” At such high St, it generates super-strong wake-rotor interactions and unsteady aerodynamics, with wake or flow responses quickly decay/dissipate in the very near wake or induction region. Maybe the authors referred to the far wake?
Thank you for this comment. Indeed, we refer to the far wake, where the flow response has already dissipated, as you noted. We will make this clear in the text.
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10. Line 264: The amplitudes should be normalized.
Thank you for this comment, we will report the amplitudes normalized by rotor diameter alongside their dimensional values.
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11. Line 332: The thrust variation could be harmonic but might not be sinusoidal; maybe justify the expression of the sine function representation.
Thank you for pointing this out. In the present text, we use “sinusoidal” and “harmonic” as synonyms, but indeed they are not. The thrust response has a dominant harmonic component at the motion frequency (see Fig. 6b), and the expression for the sinusoidal thrust refers to this harmonic component. We will clarify this.
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12. Line 350: The sampling frequency is 10 kHz, but the signal was filtered; then why not use 100 Hz for sampling?
Thank you for this comment. The 10 kHz sampling frequency was selected to ensure adequate temporal resolution of the original hot-wire signal and to avoid aliasing of higher-frequency fluctuations (mainly from electrical noise) that could affect the low-frequency content of the signal. The 100 Hz low-pass filter was subsequently applied during post-processing to remove electrical noise above it while retaining the turbulence scales relevant to the present analysis. Sampling directly at 100 Hz would not provide the same anti-aliasing protection and flexibility in post-processing. We will clarify this in the revised text.
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13. Can any evidence of statistical convergence be provided?
Thank you for this comment. We interpret it as asking us to provide evidence of convergence “of the main velocity metrics considered in the article as a function of the number of motion periods in the acquisition time.” If this is the question, it is of course valuable information, and we could add it to the appendix of the revised article.
There is an error in the text at line 356. The correct sentence is: “The acquisition time at each measurement point was 20 s, corresponding to 10 motion cycles for the 0.5 Hz excitation and 40 cycles for the 2 Hz case.”
Figure A2 shows how the mean streamwise velocity, the turbulence intensity, and the instantaneous spatially averaged streamwise velocity over the rotor region vary when computed using a number of motion cycles between 10 and 40 for the case with surge motion at a frequency of 2 Hz, at a distance of 3.5D downstream of turbine 1. The metrics in the figure were computed by gradually increasing the number of motion cycles and the time window considered in the analysis to simulate longer measurement windows. As can be seen, the mean streamwise velocity and the turbulence intensity do not vary significantly with the number of motion cycles included in the analysis. Slight variations are observed for the instantaneous spatially averaged streamwise velocity over the rotor region. The response remains periodic and nearly sinusoidal over one motion period. The maximum decreases from 0.641U0 in the 10-cycle case to 0.628U0 in the 40-cycle case, while the minimum decreases from 0.529U0 in the 10-cycle case to 0.517U0 in the 40-cycle case.
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14. Section 4.2. For inflow turbulence this low, the near-wake region could be extended to as far as 7.5D. I would suggest the authors more carefully specify this and restrict the results and conclusions to avoid mixing with the far wake properties.
Thank you for this comment. Indeed, with this low turbulence intensity the wake deficit is quite persistent downstream the turbine and in particular at the distance where the WT2 turbine is placed. We will recall this consideration in the discussion of results in section 5.4, in the conclusions, and in the abstract.
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15. Line 426-429: “Surge motion has a limited… In contrast,…” This was already reported by Duan et al. (https://doi.org/10.1016/j.enconman.2026.122028); it would be better to relate the findings. Also, the results in Lines 520-524.
The results for the wake of a single turbine are indeed aligned with the entire body of results from the experimental studies involving one turbine that are covered in the introduction from lines 46 to 79. We will underline this in the text of Sect. 4.2.2.
We were not aware of the article by Duan et al. At a first check, the experiment seems to provide results aligned with other, already cited, experiments on the wakes of single turbines. After checking it in more detail, we will consider citing it. The authors also introduce a free-rotating, bottom-fixed wind turbine in the wake of the upstream (moving) one. This downstream turbine acts as a wake sensor to detect velocity fluctuations, similarly to [4] and [5]. We can underline the comparison between the present results for the fixed downstream turbine case (WT2 fix.) and those of [4], [5], and Duan et al. in Sect. 4.3.
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16. Lines 463-464: Is there a more physics-based explanation of the “mask” effect by turbulence fluctuations?
The term “masked” was intended to describe the lower prominence of the motion-synchronized velocity component relative to other turbulent wake fluctuations.
The imposed platform motion generates a periodic wake perturbation, while other turbulent velocity components produce fluctuations that are not consistently synchronized with the motion. Phase averaging reduces these non-phase-locked contributions. At fr=0.12, the harmonic component of the spatially averaged velocity has a peak-to-peak amplitude of 0.03U0, whereas at fr=0.48 it reaches 0.10U0. The stronger coherent response at the higher frequency is therefore more clearly distinguishable from the residual variability.
To assess whether the difference arose from the number of cycles available for averaging, we repeated the phase averaging using 10 cycles for both excitation frequencies (see Fig. A1). The response at 2 Hz remained smoother than that at 0.5 Hz. Thus, the difference cannot be attributed to the number of cycles used for phase averaging.
The spectral peak at the imposed frequency confirms that a coherent response exists in both reduced-frequency cases. However, at the lower frequency, this response is less uniformly distributed across the wake, with stronger oscillations confined to particular lateral positions. Consequently, spatial averaging yields a less pronounced periodic component, making the residual turbulent fluctuations more prominent relative to the motion-induced response.
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17. Lines 485 490: The Cp and Ct values for WT2 are much lower than WT1, even based on its own “inflow”; can the authors explain? Is it due to Reynolds number effect? How do these affect the generalizability of the results and conclusions?
Thank you for highlighting this point. When referenced to the estimated local inflow, the reduction is substantially greater for the power coefficient (CP=0.11 for WT2 versus 0.28 for WT1) than for the thrust coefficient (CT=0.70 versus 0.82).
Reduction in blade-Reynolds number is a plausible contributor. Both the nominal inflow velocity and rotational speed of WT2 are approximately 63% of those of WT1, implying a comparable reduction in chord Reynolds. At these low Reynolds numbers, changes in airfoil lift and drag can strongly affect torque while producing a smaller change in thrust.
The wake inflow provides an additional possible contribution. Its spatial non-uniformity and velocity fluctuations modify the local blade inflow angles. Consequently, matching the nominal tip-speed ratio does not guarantee the same sectional operating conditions, or maximum power efficiency, as in uniform inflow.
We also clarify that the velocity of 3.1 m/s is a thrust-equivalent velocity obtained by inverting a calibrated uniform-inflow BEM relationship. It is not a directly measured rotor-area average or an energy-equivalent velocity. Normalizing power by this velocity therefore does not fully account for the non-uniform wake inflow.
These considerations limit quantitative extrapolation of wind tunnel results to full scale. The scaled blades were designed primarily to reproduce thrust and its sensitivity to inflow, rather than to ensure full-scale power-coefficient similarity. The experiments demonstrate that the relative timing of platform motion and incoming wake fluctuations affects downstream loads and power under the investigated conditions. However, the absolute coefficients, relative power gains and aerodynamic damping magnitudes should not be interpreted as direct full-scale predictions. Comparisons with the fixed configuration reduce some effects of operating at a small scale that are in common to all configurations, but do not completely remove these scaling limitations.
We will add this comment in the discussion.
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18. Line 533. What do you mean by “constructive and destructive”?
By “constructive” and “destructive”, we refer to whether the wake-induced velocity fluctuations and the velocity contribution associated with WT2 motion reinforce or oppose each other in determining the apparent axial wind speed at the downstream rotor.
A constructive interaction occurs when the two contributions reinforce the apparent wind-speed oscillation: an increase in incoming velocity coincides with upwind rotor motion. A destructive interaction occurs when the contributions partially compensate: an increase in incoming velocity coincides with downwind rotor motion.
We will clarify this in the text.
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19. Line 539-543: To say a wake is in or out of phase with motion, it would be more accurate to have correspondence PSD of the two signals. I think because wake convection is not the same as motion speed, it would be strange to compare them descriptively and qualitatively.
We agree that the phase relationship between the incoming wake fluctuations and downstream rotor motion should not be inferred directly from the prescribed phase difference between turbine motions. Wake perturbations reach WT2 after a convection delay; consequently, the relative motion phase alone does not determine their alignment with the downstream rotor velocity.
Individual power spectral densities identify the frequency content of the signals but do not retain their relative phase. A direct assessment would require synchronized velocity and motion measurements, analyzed through cross-spectral phase or an equivalent phase-resolved approach.
Such an assessment at the position operating downstream rotor was not possible with the present hot-wire arrangement. Removing WT2 would allow velocity measurements at its nominal location but would exclude the effect of its induction and therefore would not reproduce the flow experienced by the operating rotor.
Our quantitative evidence instead comes from the measured aerodynamic forces. Relative to the “WT1 fixed” configuration, the thrust oscillation amplitude increases at phi=0°, decreases at phi=180°, and takes intermediate values at the other tested phase offsets. These measurements quantify the dependence of the downstream load response on the prescribed relative motion phase, but do not independently establish the local wake-velocity phase at WT2.
We will therefore revise the passage to distinguish the measured load variations from their interpretation as reinforcement or partial cancellation of the apparent wind-speed fluctuations and remove the statement that WT2 motion is directly “out of phase with the wake acceleration”.
We propose to revise the text at lines 539–544 in this way:
Conversely, at phi=180°, the measured thrust oscillations are smaller than in the “WT1 fixed” configuration. This reduction is consistent with partial cancellation between the contributions of wake-velocity fluctuations and WT2 surge velocity to the apparent wind-speed oscillation. At intermediate phase offsets (phi=90° and phi=270°), the measured thrust amplitudes take intermediate values. These force measurements quantify the phase-dependent aerodynamic interaction between wake and downstream rotor motion, and the proposed reinforcement and cancellation mechanisms is its physical interpretation. The phase relationship between the incoming wake-velocity fluctuations and the rotor motion is influenced by the time-varying induction field generated by the downstream turbine. Further characterization of the aerodynamic interaction mechanism we described would therefore require non-intrusive velocity measurements at the WT2 rotor plane, phase-resolved with respect to the turbine motion.
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20. Section 5.2. I think the title is a bit too general, considering only two different reduced frequencies were selected and tested.
We are not sure about the problem, but we can reformulate the title as “Effect of relative motion phase on turbine–wake interaction and aerodynamic damping”. Together with the title of Section 5.1 it describes the parameters we varied without implying a comprehensive characterization of the phase/frequency space.
Let us know if it addresses your comment and if you have any other suggestions.
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21. Lines 694-696: How do these conclusions differ from existing literature? For example, Hu et al. (https://doi.org/10.1016/j.apenergy.2026.12799) and Li et al. (https://doi.org/10.1016/j.renene.2024.122062)?
The first link does not work, and we are not able to find the reference. Can you report the entire citation?
The conclusions at lines 694–696 are consistent with the article of Li et al. (2024) “Wake interaction of dual surging FOWT rotors in tandem”. Li et al. (2024) showed numerically that surge-induced coherent wake structures can enhance wake recovery and consequently increase the power available to a downstream turbine, with this effect being particularly pronounced under low-turbulence inflow conditions. The present wind tunnel tests provide experimental support for this mechanism. In addition, by considering two reduced frequencies while maintaining approximately the same amplitude of apparent-wind-speed oscillations, our results show that this effect depends strongly on reduced frequency: the wake response and associated power increase are substantially stronger at fr=0.48 than at fr=0.12.
We will revise the discussion to make the consistency with Li et al. (2024) and the specific contribution of the present results clearer.References
[1] Fontanella, A., Bayati, I., and Belloli, M.: Control of Floating Offshore Wind Turbines: Reduced-Order Modeling and Real-Time Implementation for Wind Tunnel Tests. Proceedings of the ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering. Volume 10: Ocean Renewable Energy. Madrid, Spain. June 17–22, 2018. V010T09A081. ASME.
[2] 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
[3] Schulz, C. W., Bergua, R., Branlard, E., Netzband, S., Jonkman, J., and Roberston, A.: Unsteady aerodynamics of large-scale floating offshore wind turbines in surge motion, Renewable Energy, 260, 124 977, https://doi.org/https://doi.org/10.1016/j.renene.2025.124977, 2026.
[4] Fontanella, A., Cioni, S., Papi, F., Muggiasca, S., Bianchini, A., and Belloli, M.: Experimental investigation of the effects of floating wind turbine motion on a downstream turbine performance and loads, Wind Energy Science Discussions, 2025, 1–29, https://doi.org/10.5194/wes-2025-106, 2025a.
[5] Miroux, M., Taruffi, F., and Viré, A.: Effect of floating wind turbine wakes on the thrust dynamics of a downstream turbine, Journal of Physics: Conference Series, 3224, 082 004, https://doi.org/10.1088/1742-6596/3224/8/082004, 2026.
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AC1: 'Reply on RC1', Alessandro Fontanella, 25 Sep 2026
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RC2: 'Comment on wes-2026-151', Anonymous Referee #2, 30 Sep 2026
Review of ‘Experimental evidence of wake–rotor synchronization and its effects on the aerodynamic response of tandem floating wind turbines’
The article presents an experimental study on the effects of synchronization of the wake of a downstream turbine with platform motions of an upstream one under surge motion. Aerodynamic response and wake measurements of two tandem turbines are characterized under combination of motion characteristics such as frequency, amplitude and phase of platform motions. The topic of the article is clearly of interest to the readership of Wind Energy Science, and the results are presented in a clear manner. I’d recommend the article for publication given the following concerns/comments are appropriately addressed.
- The study indicates a uniform, low shear profile with TI of 2%. Is that the case across the streamwise length of the wind tunnel test section or only upstream of the first turbine? If the flow shear or TI changes along the length of the test section, how would that affect the results from the study?
- From Fig. 1 I can see that the platform has a significant height relative to the test section. I’d imagine that would change the flow shear/TI in the turbine wake compared to a case with no platform. Is there any quantification of this effect or is this effect assumed to have insignificant effect on the flow?
- Section 2.3 mentions that hot wire probes were used for measurements and 29 measurement points were selected. Does this mean 29 probes were used simultaneously for measurements? Also, how were the probes calibrated? Please clarify this.
- The authors note that velocity measurements are carried out for 24 seconds. Is that enough for statistical convergence? This is important to establish that the differences in wake velocity between fixed and surge cases are statistically significant.
- In section 4.3, normalized coefficients of WT2 based on rotor effective wind speed show large differences from those for WT1. Is it because of reduced aerodynamic performance in the wake or some other reason? Please explain.
- Line 522, it is noted that for WT2 fixed, the thrust amplitude is smaller than WT1 fixed case. It would be beneficial to give some physical insight into why this is the case.
- Finally, I think it would be nice to put the study in context relative to existing literature on the topic with single or multiple turbines in the discussion section, especially since the study explored a limited set of frequency and amplitude. That would really enhance the scientific discussion on the topic, as it is a very rich topic with a lot of variables.
Citation: https://doi.org/10.5194/wes-2026-151-RC2 -
AC2: 'Reply on RC2', Alessandro Fontanella, 05 Oct 2026
Dear Referee, thank you for taking the time to review our article carefully and promptly. The Discussion on WESD will close on October 18th, so we would like to use the time still available to provide some initial answers to your comments. We would be pleased to hear your opinion, especially if we may have missed something or if there are any points worth clarifying.
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- The study indicates a uniform, low shear profile with TI of 2%. Is that the case across the streamwise length of the wind tunnel test section or only upstream of the first turbine? If the flow shear or TI changes along the length of the test section, how would that affect the results from the study?
Thank you for asking this question. The wind tunnel used for the experiment generates a fairly uniform inflow across the section that hosts the tests (and thus across the wind farm area in the present case). Referee #1 asked for additional information about the vertical profiles of mean velocity and turbulence intensity. We propose to report this information in the appendix of the revised article for the locations of both turbines.
Figure A1 reports these profiles, measured prior to the experiment with the turbines mounted. The inflow was characterized by measuring the streamwise velocity along vertical lines at lateral distances of yi = [-0.25, 0, 0.5, 0.75] m. The profiles at the two turbine locations are very similar, especially within the rotor area.
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- From Fig. 1 I can see that the platform has a significant height relative to the test section. I’d imagine that would change the flow shear/TI in the turbine wake compared to a case with no platform. Is there any quantification of this effect or is this effect assumed to have insignificant effect on the flow?
We do not have measurements of the wake of the same rotor with the same inflow and at the same downstream location as in this experiment, but without the robotic platform (i.e., with a simple tower), which is the information needed to address this point.
The only information we can show here is that we measured the wake of the upstream wind turbine (WT1), with a fixed tower base, along vertical lines at xi = 3.5D and xi = 4.3D, with yi = 0.15D. The offset in yi from the rotor centerline was introduced to avoid measurements directly behind the turbine tower which is not representative of a full-scale turbine (the robotic platform has a width of 0.31 m and extends from yi = –0.13D to yi = 0.13D).
The vertical profiles of streamwise velocity and turbulence intensity are reported in Fig. A2. At both xi = 3.5D and xi = 4.3D, the mean velocity profiles are fairly symmetric about the rotor axis (“Hub” in the figure) and have a relative maximum at its location. The velocity in the lower half of the wake is 5–10% lower than in the upper half of the wake. The turbulence intensity profiles have a more marked asymmetry with respect to the rotor axis. In the upper portion of the wake, the turbulence intensity increases towards the rotor edge from about 7% near the rotor axis; near the rotor edge, there is a peak attributable to the shear layer. In the lower part of the wake, the turbulence intensity decreases to 4–6%, and there is no evident shear layer. This behavior, with slightly lower recovery in the lower part of the wake accompanied by lower turbulence intensity than in the upper portion of the wake, can be attributed to a reduced exchange of momentum and mixing processes due to the ground (floor) confinement.
Although there are no measurements (with all other conditions being the same, with vs. without the platform) that allow us to quantify the effect of the platform itself, the vertical wake profiles in Fig. A2 suggest that the robotic platform does not introduce large unwanted perturbations to the flow and that the wake behavior remains consistent.
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- Section 2.3 mentions that hot wire probes were used for measurements and 29 measurement points were selected. Does this mean 29 probes were used simultaneously for measurements? Also, how were the probes calibrated? Please clarify this.
Thank you for this question. Indeed, Sect. 2.3 is not clear about this aspect. The flow was measured with two hot-wire probes mounted on a traversing system and traversed across the test section along the yi axis to cover the 29 measurement stations. The 29 measurements were therefore not simultaneous. The use of two hot-wire anemometers to measure at different positions along the yi axis assumed that the wake response to platform motion is predominantly periodic. Thus, the spatial correlation of the velocity measurements was reconstructed by phase-aligning the data with the platform motion signal, as explained in Sect. 3.2 and Appendix A.
Prior to testing, the hot-wire probes were calibrated using a reference nozzle reproducing wind speeds over the velocity range expected in the experiments with the turbines. After calibration, the measurement uncertainty of the hot-wire system was determined using a Monte Carlo simulation, accounting for uncertainties arising throughout the entire measurement process, including calibration. Factors contributing to the uncertainty included the accuracy of the data acquisition board, the pressure transducer – which influences the reference flow velocity during calibration and wind-tunnel tests – and the uncertainty of the thermocouple, which is used to adjust the hot-wire voltage for ambient temperature variations. The resulting average expanded uncertainties, at a 95% confidence level, are 0.17 ms-1 for flow speed and 0.4% for turbulence intensity.
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- The authors note that velocity measurements are carried out for 24 seconds. Is that enough for statistical convergence? This is important to establish that the differences in wake velocity between fixed and surge cases are statistically significant.
Thank you for this comment. Referee #1 also asked for additional evidence of the statistical convergence of the measurements. We agree about the importance of this information, and we propose to report it in the article Appendix.
As noted while answering Referee #1, there is an error in the text at line 356. The correct sentence is: “The acquisition time at each measurement point was 20 s, corresponding to 10 motion cycles for the 0.5 Hz excitation and 40 cycles for the 2 Hz case.”
A duration of 20 s at model scale corresponds to 20*150/2.5 = 1200 s (20 minutes) at full scale. This time corresponds to 190 revolutions of the upstream turbine rotor and 120 revolutions of the downstream turbine rotor. Regarding how the measurement time influences the main velocity metrics used in the article to quantify the effect of platform motion on the wake, we analyzed how they vary when considering an increasing length of the acquisition window (and thus an increasing number of platform motion cycles).
Figure A3 shows how the mean streamwise velocity, the turbulence intensity, and the instantaneous spatially averaged streamwise velocity over the rotor region vary when computed using a number of motion cycles between 10 and 40 for the case with surge motion at a frequency of 2 Hz, at a distance of 3.5D downstream of turbine 1. The metrics in the figure were computed by gradually increasing the number of motion cycles and the time window considered in the analysis to simulate longer measurement windows. As can be seen, the mean streamwise velocity and the turbulence intensity do not vary significantly with the number of motion cycles included in the analysis. Slight variations are observed for the instantaneous spatially averaged streamwise velocity over the rotor region. The response remains periodic and nearly sinusoidal over one motion period. The maximum decreases from 0.641U0 in the 10-cycle case to 0.628U0 in the 40-cycle case, while the minimum decreases from 0.529U0 in the 10-cycle case to 0.517U0 in the 40-cycle case.
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- In section 4.3, normalized coefficients of WT2 based on rotor effective wind speed show large differences from those for WT1. Is it because of reduced aerodynamic performance in the wake or some other reason? Please explain.
Thank you for this comment, which was also raised by Referee #1, confirming its importance.
When referenced to the estimated local inflow, the reduction is substantially greater for the power coefficient (CP=0.11 for WT2 versus 0.28 for WT1) than for the thrust coefficient (CT=0.70 versus 0.82).
Reduction in blade-Reynolds number is a plausible contributor. Both the nominal inflow velocity and rotational speed of WT2 are approximately 63% of those of WT1, implying a comparable reduction in chord Reynolds. At these low Reynolds numbers, changes in airfoil lift and drag can strongly affect torque while producing a smaller change in thrust.
The wake inflow provides an additional possible contribution. Its spatial non-uniformity and velocity fluctuations modify the local blade inflow angles. Consequently, matching the nominal tip-speed ratio does not guarantee the same sectional operating conditions, or maximum power efficiency, as in uniform inflow.
We also clarify that the velocity of 3.1 m/s is a thrust-equivalent velocity obtained by inverting a calibrated uniform-inflow BEM relationship. It is not a directly measured rotor-area average or an energy-equivalent velocity. Normalizing power by this velocity therefore does not fully account for the non-uniform wake inflow.
These considerations limit quantitative extrapolation of wind tunnel results to full scale. The scaled blades were designed primarily to reproduce thrust and its sensitivity to inflow, rather than to ensure full-scale power-coefficient similarity. The experiments demonstrate that the relative timing of platform motion and incoming wake fluctuations affects downstream loads and power under the investigated conditions. However, the absolute coefficients, relative power gains and aerodynamic damping magnitudes should not be interpreted as direct full-scale predictions. Comparisons with the fixed configuration reduce some effects of operating at a small scale that are in common to all configurations, but do not completely remove these scaling limitations.
We will add this comment in the discussion.
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- Line 522, it is noted that for WT2 fixed, the thrust amplitude is smaller than WT1 fixed case. It would be beneficial to give some physical insight into why this is the case.
Thank you for this question, which makes it evident that it would be useful to clarify how the different motion cases are constructed, their role, and what can be expected in terms of turbine aerodynamic response. These are:
- WT1: the upstream turbine undergoes motion in the free stream.
- WT1 fix.: the downstream turbine undergoes motion in the wake of the upstream turbine, which is fixed. It is similar to the “WT1” case, but instead of operating in a uniform wind field, WT2 operates in a wind field with velocity varying in space and lower on average than the free stream.
- WT2 fix.: the upstream turbine undergoes motion, and the downstream turbine is fixed. The downstream turbine works as an “inflow sensor” and is exposed to the velocity fluctuations in the wake of WT1 induced by its motion. This setup is analogous to those considered by [1] and [2].
In the “WT1” and “WT1 fix.” cases, the thrust responses of WT1 and WT2, respectively, are driven by the apparent wind speed created by platform motion. The amplitude of the thrust force response () to such motion at constant rotor speed can be written as in Eq. A1 reported in the attached document (see [3] for the derivation of Eq. A1).
In Eq. A1 is the mean streamwise velocity across the rotor (for WT1, it is the free-stream wind speed), is the normalized apparent wind speed experienced by the rotor. During one platform motion cycle at fixed rotor speed, the TSR varies between and because of the apparent wind speed created by the motion. The variation in the thrust coefficient is determined by the variation in TSR. The minimum and maximum TSRs are given by Eq. A2 and A3 reported in the attached document.
In Eq. A2 and A3 is the rotor radius and is the rotor speed. Table A1 compares the parameters and the results of Eqs. A1–A3 for turbine 1 in “WT1” case and turbine 2 in the “WT1 fix.” case. For WT1, and were obtained by interpolating the curve of the turbine measured in the free stream. For WT2, they were computed assuming the same variations as for WT1 given similar variation of TSR (values of and are similar).
As can be seen in Table A1, the amplitudes of the thrust oscillations measured in the experiment for both turbines moving in a non-modulated inflow (the free stream for WT1 and the wake of fixed WT1 for WT2) agree with those predicted by Eq. A1. The main cause of the lower amplitude of the thrust oscillations experienced by WT2 in the “WT1 fix.” case compared with those experienced by WT1 in the “WT1” case is the lower mean velocity (and thus the term 1/2 * rho * R *pi *U^2) at the WT2 rotor, caused by the WT1 wake, compared with the free stream.
In the “WT2 fix.” case, the aerodynamic response of WT2 is not driven by the apparent wind speed created by platform motion, but by velocity oscillations in the incoming flow. WT1 motion creates velocity oscillations at the frequency of its motion; these oscillations reach the WT2 rotor and produce a thrust response at the same frequency as the WT1 motion. This mechanism is discussed in [1]. The velocity oscillations in the wake at WT2 location have a lower amplitude than the velocity oscillations created by motion and therefore cause lower-amplitude thrust oscillations.
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- Finally, I think it would be nice to put the study in context relative to existing literature on the topic with single or multiple turbines in the discussion section, especially since the study explored a limited set of frequency and amplitude. That would really enhance the scientific discussion on the topic, as it is a very rich topic with a lot of variables.
We like the observation that the topic is very rich and involves many variables. Any study inevitably explores only a subset of the possible combinations of these variables. Hence, it is particularly useful to place the results of this study for a single turbine in the context of previous experimental and numerical studies that investigated a broader range of conditions or conditions different from those considered here. Similarly, the results for two turbines can be compared with numerical studies of multiple turbines conducted over a broader range of, or under different, operating conditions. This would make it possible to identify where there is agreement, and thus where the results can be safely extended, or disagreement, pointing towards the need for additional simulations and experiments to better understand the effects of some parameters.
References
[1] Fontanella, A., Cioni, S., Papi, F., Muggiasca, S., Bianchini, A., and Belloli, M.: Experimental investigation of the effects of floating wind turbine motion on a downstream turbine performance and loads, Wind Energ. Sci., 11, 1821–1851, https://doi.org/10.5194/wes-11-1821-2026, 2026.
[2] Miroux, M., Taruffi, F., and Viré, A.: Effect of floating wind turbine wakes on the thrust dynamics of a downstream turbine, Journal of Physics: Conference Series, 3224, 082 004, https://doi.org/10.1088/1742-6596/3224/8/082004, 2026.
[3] C.W. Schulz, S. Netzband, U. Özinan, P.W. Cheng, M. Abdel-Maksoud, Wind turbine rotors in surge motion: new insights into unsteady aerodynamics of floating offshore wind turbines (FOWTs) from experiments and simulations, Wind. Energ Sci. 9 (2024) 665-695, http://dx.doi.org/10.5194/wes-9-665-2024.
Data sets
Wind tunnel measurements of loads and wakes in tandem floating wind turbines under harmonic surge motion Alessandro Fontanella et al. https://doi.org/10.5281/zenodo.19492347
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- 1
The manuscript presents a valuable and timely experimental dataset regarding tandem floating offshore wind turbine aerodynamics, but it requires a comprehensive and rigorous revision before it can be considered for publication. In particular, I would suggest the authors include more relevant literature to clearly identify the existing body of knowledge, gaps, and their own novelty (especially since many results were reported by previous studies). Specific comments are provided as follows.
1. It seems that the lowest tip-swept point/clearance of the turbine model is only 6.9cm from the platform; any evaluation of this effect?
2. Lines 160-165: Maybe explain or cite a reference regarding the rotor design and where this analysis was made.
3. Lines 168-169: Please specify the dynamic parameters for the motion platform/motor, or cite relevant references.
4. Why was an inflow with no-shear and 2% turbulence intensity used? For the reason of revealing pure motion effects, shouldn’t it be more appropriate to use laminar flow?
5. Line 176: Any evidence or reference that shows the profiles of velocity and turbulence intensity? Seems it is quite close to the ground that part of the model would be immersed in the wall boundary layer.
6. Lines 197-198: I would expect evidence or references regarding this. And how would fixed rotor speeds make the results differ from varying ones? Which scheme is more likely to be used in reality?
7. Lines 232-234: “At full scale…” References should be provided to support the ranges of motion frequencies.
8. Lines 247-248: “…, while aerodynamics… scale linearly…” Why does aerodynamic force scale linearly with frequency? Is it applicable to all ranges of frequencies (or St)?
9. Lines 250-251: “Previous…negligible.” At such high St, it generates super-strong wake-rotor interactions and unsteady aerodynamics, with wake or flow responses quickly decay/dissipate in the very near wake or induction region. Maybe the authors referred to the far wake?
10. Line 264: The amplitudes should be normalized.
11. Line 332: The thrust variation could be harmonic but might not be sinusoidal; maybe justify the expression of the sine function representation.
12. Line 350: The sampling frequency is 10 kHz, but the signal was filtered; then why not use 100 Hz for sampling?
13. Can any evidence of statistical convergence be provided?
14. Section 4.2. For inflow turbulence this low, the near-wake region could be extended to as far as 7.5D. I would suggest the authors more carefully specify this and restrict the results and conclusions to avoid mixing with the far wake properties.
15. Line 426-429: “Surge motion has a limited… In contrast,…” This was already reported by Duan et al. (https://doi.org/10.1016/j.enconman.2026.122028); it would be better to relate the findings. Also, the results in Lines 520-524.
16. Lines 463-464: Is there a more physics-based explanation of the “mask” effect by turbulence fluctuations?
17. Lines 485 490: The Cp and Ct values for WT2 are much lower than WT1, even based on its own “inflow”; can the authors explain? Is it due to Reynolds number effect? How do these affect the generalizability of the results and conclusions?
18. Line 533. What do you mean by “constructive and destructive”?
19. Line 539-543: To say a wake is in or out of phase with motion, it would be more accurate to have correspondence PSD of the two signals. I think because wake convection is not the same as motion speed, it would be strange to compare them descriptively and qualitatively.
20. Section 5.2. I think the title is a bit too general, considering only two different reduced frequencies were selected and tested.
21. Lines 694-696: How do these conclusions differ from existing literature? For example, Hu et al. (https://doi.org/10.1016/j.apenergy.2026.127999 ) and Li et al. (https://doi.org/10.1016/j.renene.2024.122062 )?