the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 20 Feb 2026
Influence of the inflow conditions on the dynamics of a floating wind turbine wake under harmonic surge motion
Abstract. Floating Offshore Wind Turbines (FOWTs) are projected to undergo substantial expansion in the coming decades. However, the motion of their supporting platforms due to mooring lines and wave interaction makes it difficult to predict their wake dynamics. The vortex ring structure produced during surge motion has been subject of study for nearly a decade now but there are still many features to bring to light. As most of the studies have been under idealized, uniform flow there is little knowledge on how this structure behaves under Atmospheric Boundary Layer (ABL) flow. In this work, the authors propose to study this structure under three different inflow conditions: laminar and turbulent uniform flows, and ABL flow. Large Eddy Simulations are carried out in combination with an Actuator Disk (AD) as a wind turbine model, with a focus on surge motion and a Strouhal number ranging between 0 and 0.47. In order to quantify the energy of the vortex ring structure, Proper Orthogonal Decomposition (POD) is applied to a vertical plane parallel to the AD axis. A good visualization of the structure is achieved for all cases, and the energy of the vortex ring structure exhibits a local maximum for turbulent and ABL flows, with the highest energy at Strouhal number 0.30 and 0.32, respectively. However, the local maximum is narrower in the ABL case than in the turbulent one. Also, due to the presence of strong turbulent structures in ABL flow, the energy present in the vortex ring structure is considerably lower in this case than under uniform turbulent flow. For the laminar case, the POD method allocates almost 99.9 % of the energy to modes related to the vortex ring structure, as no other strong structures arise in the wake. A meandering phenomenon is detected under low-turbulence and ABL flows. In the first scenario, meandering is initiated by inflow conditions, while in the second, it is the consequence of the interplay between shear flow and surge motion. The study is replicated in a horizontal plane at hub height, thereby demonstrating that for the low-turbulence flow, meandering occurs with equal intensity in all directions. Conversely, in ABL conditions, lateral meandering is unrelated to the vortex ring structure. Finally, phase average is carried out to evaluate how the structure propagates in each case. The results obtained indicate a faster decay of the structure for the non-laminar inflow cases, although the impact on the growth rate is contingent on the energy content of the vortex structure for each surge frequency. Further analysis indicates that the wake is modulated by the surge motion, manifesting as expansions and contractions, for the laminar and low-turbulence cases. In contrast, an inclination of the structures towards the flow direction is identified in the ABL conditions, attributable to the shear flow.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Wind Energy Science.
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. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: open (until 20 Mar 2026)
- RC1: 'Comment on wes-2026-43', Anonymous Referee #1, 24 Feb 2026 reply
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RC2: 'Comment on wes-2026-43', Anonymous Referee #2, 02 Mar 2026
reply
Dear Authors,
I was invited by the Associate Editor to review your manuscript and was pleased to accept, as the topic is of strong interest to me and closely aligned with my recent research activities. In recent years, the wind energy community has devoted increasing attention to the aerodynamics and wake interactions of floating wind farms, making the subject of this manuscript both timely and relevant to the readership of Wind Energy Science.
The results presented contribute to the growing body of work developed by several research groups in this area, and the findings are of clear interest. However, the manuscript would benefit from improvements to enhance its clarity and impact. In particular:
- The main contributions should be more clearly articulated in the abstract and introduction to better guide the reader and emphasize the novelty of the work.
- The rationale behind the selection of the simulated cases should be explained in greater detail.
- A brief introductory description of the data analysis techniques employed would improve accessibility for readers who may not be specialists in these methods.
- Further clarification is needed regarding the validity and representativeness of results obtained using an actuator disk model at model scale, particularly in relation to full-scale, bladed wind turbines.
Overall, I believe the manuscript is suitable to proceed in the review process at Wind Energy Science and may be considered for publication, provided that the authors adequately address the reviewers’ comments.
General comments
- Section 2.4 – Cases Analysed. I recommend adding a brief discussion linking the selected Strouhal numbers (St) to the characteristic frequencies of floating wind turbines in the 10–15 MW range. When combined with near-rated wind speed conditions, the St values considered in this article are expected to correspond to the frequency range associated with the rigid-body modes of spar or semisubmersible platforms. Providing this context would help readers better understand the physical relevance of the selected cases. In addition, it would be useful to clarify why higher reduced frequencies (potentially representative of the wave frequency range, where large platform motions may occur due to wave excitation) were not considered.
- Section 4. The presentation of the POD results could be made more didactic to benefit readers who may not be familiar with this type of analysis. For instance, further explanation could be provided on why certain modes appear as opposite pairs and how they should be physically interpreted. This is particularly important given the paper’s structure, in which similar types of results are presented repeatedly for different cases. I recommend including a concise introductory explanation of how to interpret POD results, either at the beginning of Section 4 or by using the results in Section 4.1 as a guiding example, to support the reader throughout the remainder of the section.
- L512: “this phenomenon … of the wake”. I consider this one of the most interesting findings of the study, and it deserves greater emphasis in both the abstract and the conclusions. The result appears to be relevant to any situation in which the free-stream inflow is non-uniform, which broadens its potential impact.
- L560: “the present study … in previous experiments”. This statement would benefit from further clarification. It would be helpful to more explicitly explain the relationship between the present results and those reported in previous experiments, highlighting similarities, differences, and possible reasons for any discrepancies.
Specific comments
- Abstract: The abstract is long. I recommend shortening it to focus more clearly on the innovative aspects of the work and the most significant results.
- L2: “due to mooring lines”: The motion is more directly related to the high compliance of the floating foundation rather than to the mooring lines alone. Please consider clarifying this point.
- L30: “movements”: Please specify whether these are rigid-body motions or motions associated with the overall platform response.
- L33: “by the surge frequency”: Quasi-static effects are not dependent on the motion frequency. Rather, they are driven by the apparent wind speed experienced by the rotor, which is induced by platform motion regardless of its frequency. I suggest revising this statement accordingly.
- L59: “this structure”: It is not clear what “the structure” refers to. Please be more specific.
- L101: “data”: Consider replacing “data” with a more precise term, such as “measurements of velocities” or another description that clearly specifies the type of data used.
- L203: “10s are left … following 40s”: How do these time intervals relate to full-scale conditions? Providing this information would be valuable, particularly for readers interested in applying a similar methodology to full-scale turbine simulations rather than a small-scale experimental setup.
- L204: “4D”: Why was 4D selected? Are the results obtained at 4D representative of other downstream distances? Please clarify.
- L213: “Then, the two mesh refinements … are recorded”: The simulation procedure is not entirely clear. Please clarify whether this refers to a single continuous simulation with successive mesh refinements or to multiple separate simulations that were later combined.
- L221: “experimental values”: Please make explicit that the experimental results were used as the reference or target for the simulation setup.
- L242: “a vertical plane”: It seems that multiple vertical planes may have been considered. If so, please use “vertical planes,” or clarify that the same analysis is applied to several planes.
- L527: “new”: Please clarify in what sense this is “new” (e.g., new methodology, new physical insight, new configuration, or new application).
Citation: https://doi.org/10.5194/wes-2026-43-RC2 -
RC3: 'Comment on wes-2026-43', Anonymous Referee #3, 11 Mar 2026
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The paper investigates how inflow conditions affect the wake of a floating offshore wind turbine model undergoing harmonic surge motion, using LES with an actuator-disk representation under laminar, low-turbulence and ABL inflows. The overall quality of the manuscript is good. Since the other two reviewers have already pointed out several interesting observations, I will focus on a few specific comments on topics I believe would benefit most from further effort, followed by some minor technical corrections I identified while revising the paper.
Specific comments:
- L159, “The porous disk is assumed to have a constant CT”. In my opinion, this assumption is correct in the case of a fixed inlet velocity and a still platform, but not so strictly in the cases analysed in the paper, since the relative velocity of the disk changes together with the platform motion. Perhaps the authors have previously observed that such changes do not come with a significant change in the value of CT. If this is the case, I suggest adding a brief explanation to strengthen the validity of the assumption. Furthermore, a discussion of a possible loss of generality (if any) when extending results of an actuator disk to a three-bladed rotor would help clarify the applicability of the framework presented in the paper.
- The choices described in section 2.3 regarding the dimensions of the computational domains should be clarified more in details. For example, if the intent is to compare experimental and numerical results to obtain a validation, it is not clear why the dimensions of the domain are smaller than those of the wind tunnel. Also, clarifications should be required to support the choice of a 5D height for the ABL domain, as well as for the use of different boundary conditions for the top and bottom walls.
- Section 2: The dinstinction between the three conditions is appreciated and essential to understand the following of the paper, including section 2.3 for instance. IS shear considered in the low turbulence case?
- The conclusions drawn from the mesh convergence study presented in section 3 may be leave room for discussion, as the mesh #2 does not seem to be fully converged (for example in the shear layer between 0.75 and 0.25 D). Furthermore, demonstrating the level of convergence of more than one section downstream would help to provide a stronger generality to the conclusions of the convergence study.
Technical corrections:
- L3, possible typo, I think “has been the subject of study” would sound better.
- L4, possible typo, I think “as most studies” would sound better.
- L10, typo, “with the highest energy at Strouhal numbers30 and 0.32, respectively”.
- L54, typo, “… six degrees of freedom…”.
- L60, typo, “Due to these reasons”.
- Figure 4 caption, typo, “All profiles are zoomed in the refined region. The dotted red…”.
- L260, typo, “see Table 2”.
- L260, possible rephrasing for improved clarity, i.e. “In all figures, the most energetic modes include pairs with similar energy content”.
- L283, possible rephrasing, “ST = 0.32 exhibits higher energy in the first pair of modes and lower energy in the harmonics”.
- L310, please rephrase “The range of frequencies in these modes, not shown here, are a great match with…” or correct the verb “are” with “is”.
- L339, typo, “mode pairing”.
- L391, typo, “This comprehensive comparison with laminar and low-turbulence inflows has revealed …”
- L395, perhaps “ABL inflow conditions” sounds better than “ABL flow”.
- L444, typo, “the local mean velocity is subtracted” or “the local averaged velocity is subtracted”.
- L503, typo, “… due to the surge motion”.
- Coherence should be maintained with British or American English, since in the manuscript terms like visualise/visualize or analyse/analyze are present at the same time. The same applies to the terms disc/disk.
Citation: https://doi.org/10.5194/wes-2026-43-RC3 -
RC4: 'Comment on wes-2026-43', Anonymous Referee #4, 11 Mar 2026
reply
Dear authors, dear editor,
the considered work describes an LES-AD study on a surging wind turbine rotor under three types of inflow: laminar/uniform, low-turbulence/uniform, and high-turbulence/ABL. A selected set of harmonic surge motions is utilised to investigate whether coherent structures appear in the wake of the turbine from 2–10 D. These structures could be identified consistently by POD analysis and phase averaging, while the level of turbulence decreased their relevance for the overall wake behaviour. In the ABL cases, the wind shear modified the observed pulsating structure, which is finally interpreted as vertical wake meandering.
From my point of view, the manuscript is a valuable contribution to the analysis of the impact of FOWT motions on wake behaviour and should definitely be considered for publication in WES. The topic is very timely, and the work provides a strong analysis of the physical phenomena. The manuscript is well written, contains very few typos, follows a clear line of argumentation, and contains suitable figures.
However, the manuscript could be further improved, as it has some weaknesses regarding the general assumptions, such as motion or inflow conditions and turbine specifications. Please find my detailed comments below and in the attached PDF.
Best,
reviewer #4
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Comments:
General:
The study is obviously designed in a way that the experiments of Schliffke et al. could be reproduced. However, no comparison with their results has been performed, which is quite surprising. Please explain in the paper, why this is the case and why you still choose to replicate the rest of the setup. I guess this is due to the fact that Schliffke et al. Considered a Ct of 0.5, which is rather low. However, at least a short validation case with Ct=0.5 and a comparison with the experimental data would be very beneficial. This uncertainty (what is actually replicated here and why?) remains through the paper and should be clarified to strengthen the red line of the study. It is also very important to discuss the chosen motion conditions. They have been adapted from Schliffke, however, according to my understanding, they represent a rather small 2MW rotor at very slow motions (between 100 and 16s of motion period at 8m/s) and quite large motion amplitudes (12.5% of the rotor diameter). The chosen motion parameters should be set into the context of modern turbines.
Abstract:
The abstract is comparatively long and it is recommended to make it shorter. The description of the simulation study is quite detailed for an abstract, however, still difficult to follow since it seems that the authors try to explain the complete study in detail here. It is recommended to reduce the level of detail and focus on the basic idea of the simulation study and the main findings, while leaving out how this was achieved. It would be beneficial to move a bit more towards a bird’s eye perspective.
Introduction, numerical modelling and experimental studies:
A number of relevant publications in the field are listed and described here. However, only very few conclusions relevant for this study are drawn from the description. It would be beneficial to really discuss some of the studies in the context of the present work. For example, the role of the motion frequency is not really discussed. The suitability or limitations of the used method could also be discussed using the literature.
Solver:
It is written that „a newly implemented solver in OpenFOAM (OpenCFD-Ltd, 2004), which was constructed using the SOWFA libraries as a basis (Churchfield et al., 2012a, b)“ was used in to perform the simulations. First: Is this an in-house development? If yes: Please either describe the implementation or give a source. What is implemented and how is it verified? What part is taken from other sources and what is the own contribution? If no: Please give a source, where the actual implementation is described. If you use the SOFWA code, the version of the code should be named and the source for the actual implementation should be cited (at least the github repository).
Inflow conditions:
A discussion on the chosen ABL parameters is missing: Is there only one ABL? What is special? What is chosen and why?
POD laminar:
„Furthermore, the frequencies exhibited in the modes, as illustrated in Fig. 9a, show a smooth distribution across a range of frequencies. Additionally, modes 3 and 4 display a complementary spectrum when compared with modes 1 and 2. Modes 5 to 10 (not shown here) also demonstrate analogous complementary behaviour with regard to frequency. This finding suggests that the observed structure is inherent to all frequencies within a range, thereby confirming the absence of any structure being advected that can be associated with a specific phenomenon.“
This seems a bit inconsistent to me. Actually, Figure 8 shows clear structures in modes 1-4. The corresponding Fourier spectra actually show that there is not one isolated frequency associated with the modes, however, the range of corresponding dominant frequencies is rather narrow (St~0.2-0.55), and far from being distributed randomly. Therefore, I cannot really follow, why there should be an „absence of any structure being advected that can be associated with a specific phenomenon“. The fact that this structure seems to be rather weak (6 magnitudes smaller) seems convincing on the other hand. However, when summing up the Fourier amplitudes in a range of St e [0.2-0.55], I would expect to see a similar (or even higher) value compared to the other two cases. Let’s assume that there are structures generated in case of St=0; however, these structures would be related to some kind of ‚natural‘ meandering or sth. similar. In this case, the structures would not necessarily evolve at the exact same frequency, since their generation is somehow of a statistical nature. As known from other studies, such meandering should be pronounced around St~0.3. In this case, the assumed structures in the wake would be present, however, their frequency and lateral expansion would slightly vary over time. A Fourier transform on this (let’s say for a time of 40s), would actually not show a clear peak, but more a stochastic distribution around St~0.3. From my point of view, this could be in line with what we see in Figure 9a. If this is true, we would actually have some stable structures in the wake. which slowly vary their frequency. However, due to the long window of time, we cannot exactly see them in the POD analysis, since it requires the structures to happen at the EXACT same frequency and lateral expansion.
POD turbulent:
For the St=0 case, the maximum frequency of Mode 1 occurs somewhere around 0.075Hz, which is far from the maximum frequency observed in the laminar case. Does this frequency somehow relate to the turbulence length scale of the low turbulence case (~6D)?
Phase averaging:
I understood that the phase averaging in Fig 21 was performed at the motion frequency (St=0.32). Is this correct? If yes, I would expect a behaviour in Fig. 21 (a), which is somehow similar to modes 1 and 2 in Figure 8 (c), since those occur at the exact same frequency. However, in Fig 21 (a), the distance in downstream direction between minima and maxima of the pulsation is approximately twice as high, which indicates a much lower frequency (half the motion frequency?). Maybe I am getting something wrong here. It would be helpful if you could explain this.
Conclusion:
„Overall, the study highlighted that the vortex ring structure exhibits a significantly different behaviour depending on the inflow conditions. In particular, the presence of ABL shear not only modifies the spatial shape of the modes but also strongly influences their amplification and energy distribution.“
From my point of view, this has not been shown directly. I guess, the fact that the „ABL shear … strongly influences their amplification and energy distribution“ is derived from Figure 12 (a-c). Here, it is shown that the amplification strongly changes from the low-turbulence to the ABL case. However, the difference between the low-turbulence to the ABL flow is not only the ABL shear, but also a significant increase of the overall turbulence level. Therefore, I would not be able to distinct if the shear or the increased level of turbulence caused this.
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Dear authors,
thank you for your valuable contribution to Wind Energy Science. I found the paper quite interesting and well presented. After carefully reviewing the manuscript, I have some questions that should be adressed before publication. Please find them in the attached document.