Wake steering under inflow wind direction uncertainty: an LES study

Hodgson, Emily Louise; Andersen, Søren Juhl

doi:10.5194/wes-11-2173-2026

Articles | Volume 11, issue 6

https://doi.org/10.5194/wes-11-2173-2026

© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/wes-11-2173-2026

© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 11, issue 6

Research article

|

19 Jun 2026

Research article |

| 19 Jun 2026

Wake steering under inflow wind direction uncertainty: an LES study

Emily Louise Hodgson and Søren Juhl Andersen

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Final revised paper (published on 19 Jun 2026)
Preprint (discussion started on 19 Nov 2025)

Interactive discussion

Status: closed

RC1:
'Comment on wes-2025-243', Anonymous Referee #1, 23 Dec 2025
I commend the authors for a very well-written manuscript and well-crafted narrative, including the literature review to introduce the problem and recent advances. I agree with much of the authors’ methods, results, and conclusions presented and I recommend the manuscript for publication with a few minor revisions that I’ll note here, but I do have a couple questions for the authors to consider and maybe add clarifying notes.
Suggested Revisions
Line 73: What does it mean that Simley et al. “used a similar approach in reverse” to Rott et al.? Based on the brief descriptions of the two methods it is unclear what this phrase means and it confused me slightly.

Line 133: A constant temperature profile with height of 288.15 K is applied, so I believe dT/dz = 0.

Figures 3-5: I would suggest referring to the plane position as 0.5D instead of 1R because R hasn’t been defined yet.

Line 267: Is this semicolon here by mistake?

Questions
Line 113: Is there a reason why a 22MW turbine was chosen in this case study? Do the authors expect any changes in the trends of their results for a smaller turbine, say in the 5MW range, that is more common presently?

Line 151: What does “the cell sizes are stretched to the domain boundaries” mean? I assume that there is more than one cell outside of the refined region, so does this mean that the cells are progressively stretched from the refined size to the background size?

Line 154: How were these times decided upon? Are the wakes considered developed after a certain number of flow through periods at the rotor height, and was any analysis of the wake velocity deficits used to make this determination?

Line 221: What does area-normalized histogram mean? Is this the wind direction averaged over the rotor area?

Line 227: Which statistics are calculated with a moving average, and which are not? There are several means and standard deviations introduced in the text and I found myself getting mixed up, especially here where there are two different standard deviations with a 1 minute time average.

Figure 10: My main conceptual question regards this idea of how additional wind direction uncertainty is estimated based on the existing simulations. The authors refer to the Rott and Simley papers, so I recognize that this method has been applied before, but I am skeptical of how well this Gaussian process approach can capture all of the non-linearities of the power response to wind direction. I agree with the trends that are elucidated by this experiment, namely that increased wind direction uncertainty reduces the benefits or viability of wake steering. I would be interested in seeing the actual power production results from simulations with the increased standard deviation, but this would be outside the scope of the current work. Perhaps this concern already falls under the discussion starting at Line 430, or the authors could add a note discussing this to Section 4.1.

Line 374: I agree that it is an interesting idea to consider yawing to decrease fatigue loads despite a decrease in total power, but I wonder if yawing would increase other relevant loads on the turbines besides the flapwise bending moment?
Citation: https://doi.org/10.5194/wes-2025-243-RC1
RC2: 'Comment on wes-2025-243', Anonymous Referee #2, 10 Jan 2026

Comments on "Wake steering under inflow wind direction uncertainty: an LES study" by Hodgson and Andersen

In the manuscript by Hodgson and Andersen, the authors conduct a numerical study on the effect of wind direction uncertainties on wake steering. The LES study considers a single column of 4 turbines in a conventionally neutral ABL, and three wake steering configurations. Six different inflow wind directions are considered by changing the layout of the turbines in the same ABL condition. Their findings indicate that wake steering is beneficial within a narrow window of 7.5 degrees, and using Gaussian convolution to extrapolate to larger amounts of wind direction uncertainty leads to a decrease in the effective window and the overall power gains.

Overall, the study is systematic and methodically conducted, and the conclusion the authors deliver is an important point which deserves attention -- wake steering is very sensitive to wind direction and inflow condition uncertainty, and gaining control over these uncertainties will be important for wake steering to be successful. However, there are some considerations which might help to strengthen the study and help generalize its findings, or at least point to several areas which are necessary for future studies.

Major points

- The current study is focused on a single column of turbines with 7D streamwise spacing. While this is a relatively clean and simple configuration for this study, realistic wind farm layouts may see interactions with neighboring columns, such that at larger wind directions, downstream waking can occur even if it is not from the turbine immediately upstream. For the larger offshore turbines like the IEA22MW, 7D spacing (1988 m) may not be achievable, and turbine spacings may be closer. In section 4.0, a discussion of shorter turbine spacings is presented, but it may be worth considering how these findings hold deep within the center of larger wind farms, and how much the benefits might decrease with neighboring, closely spaced turbines.

- The neutral ABL used in this study, while convenient to setup and use in LES, may not be a representative condition for offshore wind farms in reality. Truly neutral conditions may only last for a few minutes per day as measured in the field, as the ABL transitions from stable to unstable conditions or vice-versa. However, simulations in this study are run for 5100 of flow time, with averages over 3600 seconds used for the statistics, which produces very clear contrasts between the different wake steering configurations. This idealization is discussed in section 4.1, where it is mentioned that more common 5 or 10 min statistics contribute to the uncertainty in measurements. However, it may be worth discussing how an LES study might be conducted so that more realistic wind direction, wind speed, or ABL stability changes can be taken into account, and how an optimal wake steering strategy could be determined in the face of these complex uncertainties.

- In section 3.2, a Gaussian convolution approach is used to extrapolate the wind direction uncertainty from the 2.3 degrees in the LES to higher values of uncertainties. In this analysis, it may be important to acknowledge the larger values of wind direction variability can be connected to changes in the inflow atmospheric stratification, which in turn change the wake behavior. As an example, unstable ABL conditions might have larger values of \sigma_WD, but are also associated with faster wake recovery and shorter wakes. Thus, it may not be appropriate to extrapolate the neutral LES results to larger WD uncertainties while assuming the wake properties are constant.

- The LES simulations use an actuator disk approach to model the IEA22MW turbine forces in a highly yawed configuration (-20 degrees), and both the power and DEL are reported based on the HAWC2 solver coupled to the AD model. It may be useful to include additional information on the performance of the AD model under such conditions, compared to higher fidelity models such as actuator line models. Of potential concern is whether the blade loading is accurately captured under high yaw, and thus if the turbine torque or thrust are properly calculated through the CFD (and thus, if the downstream wake is properly initialized).

Minor points

- Introduction, line 42, minor stylistic point "Concerning the former, imperfect response to a control input can occur" -- imperfect may not be the best adjective to use here, as it implies there is a perfect yaw control response.

- Section 2.2 -- It may be worth explicitly stating if a yaw controller is active during the IEA22MW simulations -- it appears that a constant, fixed yaw is always applied to each turbine. How much would the wake steering benefits change if the yaw controller is active? By default, the IEA22MW turbine, if using the ROSCO turbine controller, activates yaw only if misalignment exceeds 4 degrees, so it may be interesting to consider how long it takes the turbines reach their intended set point once the wake conditions are detected.

- Section 2.3, line 133: "temperature profile dT_0/dz = 288.15K" -- that is probably a typo, it might be temperature profile T(z) = 288.15

- Section 2.3 -- Some additional information on how the ABL conditions were chosen may be useful to the reader, including the choice of the geostrophic wind values, the wall roughness, etc.

- Section 2.3 -- It may be useful to add how the lower boundary conditions were enforced in the precursor ABL and wind farm simulations.

- Section 2.4 -- line 150: "dx = dy = dz = 32/D" -- possibly a typo, and meant D/32

- Section 2.3/2.4 -- What were the mesh sizes and timesteps used in the simulations?

- Section 3.1 line 222 -- typo, "infront" is two words

- Section 3.1, figure 5 -- The histograms of the wind direction were created by sampling a single point velocity at 0.5D upstream of the turbine rotor. A single point, upstream measurement of wind direction may be susceptible to influences from turbine induction and veer, and is generally not available to turbines operating in the field. It may be interesting to consider a measurement of the wind direction based either on rotor disk averages, or for more realism, and virtual nacelle vane measurement that would be used by the turbine controller.

- Section 3.1, line 234 -- "for WD = 8 degrees, there is very little wake impingement on the downstream turbines". This conclusion may be limited to this specific configuration of a single column of 4 turbines. In a larger wind farm array, for instance, in a 4x4 array, even if there is not direct downstream waking, there may be wake effects from neighboring turbine columns (see major point above).

- Section 3.2, line 253 -- "tends back to that of the baseline" -- optional, perhaps reword this sentence to avoid awkward phrasing

Citation: https://doi.org/10.5194/wes-2025-243-RC2
AC1: 'Comment on wes-2025-243', Emily Louise Hodgson, 20 Feb 2026

Thanks to both reviewers for their insightful and constructive comments. Responses to all suggestions are contained in the attached PDF.

Citation: https://doi.org/10.5194/wes-2025-243-AC1

Peer review completion

AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload

AR by Emily Louise Hodgson on behalf of the Authors (20 Feb 2026) Author's response Author's tracked changes Manuscript

ED: Publish subject to minor revisions (review by editor) (17 Mar 2026) by Julie Lundquist

Thank you for your thoughtful revisions to the manuscript. While generally most of the reviewer comments were considered and responded to carefully, three outstanding issues should be addressed by the authors for my review before acceptance.

1. Reviewer 2 raises two related concerns regarding the role of atmospheric stability and inflow stratification in determining wake recovery and the effectiveness of wake steering. In your response you indicate that this limitation has been acknowledged in Section 4.2, but the revised manuscript does not explicitly discuss atmospheric stability, and the current wording focuses primarily on the diurnal cycle. These are not equivalent, and the discussion should more clearly address stability as a governing physical factor.

Please revise the manuscript to explicitly acknowledge that atmospheric stability and inflow stratification strongly influence turbulence intensity, shear, and wake recovery, and therefore can substantially modify both wake dynamics and the effectiveness of wake steering strategies. Because the simulations in this study employ a conventionally neutral boundary layer inflow with relatively low turbulence intensity and mild veer, the results represent a limited subset of atmospheric conditions that are generally favorable for wake steering. The manuscript should therefore clearly state that the conclusions may not directly extend to more strongly stable or convective boundary layers, where wake recovery rates and wake steering performance may differ substantially. Adding a short paragraph explicitly framing this limitation and clarifying how the chosen inflow conditions relate to the broader range of atmospheric stability regimes encountered in real wind farms would more completely address this concern.

2. Reviewer 2 also raised an important question regarding the use of an actuator disk representation rather than an actuator line model. While your response to the reviewer provides a clear and well-reasoned explanation, including a helpful supporting figure, this discussion currently appears only in the response-to-reviewers document and not in the manuscript itself.

Because the choice of turbine representation can influence near-wake structure and therefore potentially affect wake steering predictions, I recommend incorporating a brief version of this explanation directly into the manuscript. In particular, the manuscript should explicitly acknowledge the implications of using an actuator disk model, explain why this approach is appropriate for the objectives and scales considered in this study, and clarify any expected limitations relative to actuator line approaches.

A concise paragraph in the methods section summarizing the key points you made in the response would strengthen the manuscript and ensure that readers who do not see the review correspondence can understand and evaluate this modeling choice.

3. Additionally, please clarify the application of the log-law in both the precursor and turbine-resolving simulations in Section 2.3, as requested by Reviewer 2. If this point raised a question for one reader, it is likely that other readers may have the same question. Providing a brief clarification in the manuscript will help ensure that the modeling approach is clearly understood by the broader readership.

Finally, you may consider changing the color tables that you use for Figures 2-5 per the guidance at https://publications.copernicus.org/for_authors/manuscript_preparation.html#figurestables, since those figures could not be understood by readers with some types of colorblindness according to https://www.color-blindness.com/coblis-color-blindness-simulator/

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AR by Emily Louise Hodgson on behalf of the Authors (17 Apr 2026) Author's response Author's tracked changes Manuscript

ED: Publish as is (26 Apr 2026) by Julie Lundquist

ED: Publish as is (29 Apr 2026) by Paul Fleming (Chief editor)

AR by Emily Louise Hodgson on behalf of the Authors (04 May 2026) Author's response Manuscript

Short summary

This work investigates the impact of wind direction uncertainty on wake steering, a promising flow-control strategy that aims to increase the efficiency of wind farms, using high-fidelity computational fluid dynamics. It concludes that wake steering is sensitive to both bias and uncertainty in inflow wind direction due to having a relatively small range over which gains are predicted and showing significant decreases in peak power output with increasing wind direction uncertainty.