the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 24 Oct 2025
PhyWakeNet: a dynamic wake model accounting for aerodynamic force oscillations
Abstract. Advanced wind energy technologies require predictions of the dynamic behaviour of wind turbine wakes. In this work, we present a dynamic wind turbine model PhyWakeNet, a physics-integrated generative adversarial network-convolutional neural network (GAN-CNN) model for wind turbines under aerodynamic force oscillations. The model combines three interconnected submodels for the time-averaged wake, wake meandering, and small-scale wake turbulence. The time-averaged wake model derives from mass and momentum conservation based on the concept of momentum entrainment, which is computed based on the wake meandering and small-scale wake turbulence models. The wake meandering is captured through conditional GAN-reconstructed spatial modes and neural network-enhanced dynamic system for temporal evolution, while the small-scale wake turbulence is generated via a CNN based on the time-averaged wake, wake meandering, and inflow turbulence. Validation on wind turbine wakes under active control demonstrates the model's capability to predict frequency-dependent wake responses, velocity deficits, and turbulence kinetic energy. The model accurately captures temporal variations of key characteristics like instantaneous wake centers and velocity deficits, enabling potential applications in wake management to mitigate aerodynamic loads and power fluctuations in wind farms.
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: closed
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RC1: 'Comment on wes-2025-189', Anonymous Referee #1, 03 Nov 2025
- AC1: 'Reply on RC1', Xiaolei Yang, 11 Jan 2026
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RC2: 'Comment on wes-2025-189', Anonymous Referee #2, 06 Nov 2025
The manuscript presents a hybrid framework for developing a dynamic wake model that integrates first principles with machine learning (ML) techniques. The ultimate goal is to enable dynamic single-turbine wake modeling accounting for aerodynamic force oscillations. The authors leverage three sub-models to capture time-averaged wake, wake meandering, and small-scale wake turbulence. Some submodels are trained using LES data, and the results show generally good agreement with the ground truth. The work addresses an important problem in wind-energy modeling and has potential for impactful contributions. However, there are several points that need to be addressed to strengthen the manuscript.
Major comments:
1. A primary concern is that the ML models are mostly treated as "black box. There is no discussion or demonstration of explainability, such as feature importance or SHAP tools. Since two of the submodels rely heavily on ML and directly affect the first submodel and overall wake predictions, the lack of explainability limits the credibility and understanding of the framework. It is strongly recommended to include an assessment of how the ML predictions are derived and how dependent they are on inputs.
2. The manuscript lacks a comprehensive review of recent literature in data-driven wake modeling, especially regarding generalization and explainability of ML-based wake predictions. Providing a critical comparison would clarify the novelty of this work.
3. Please provide a quantified comparison of the onset of wake meandering rather than relying on qualitative assessment from the results in Figure 12.
4. Regarding Figure 14: I agree with the authors that the model struggles more in predicting the wake centerline velocity deficit than the wake center position. The model captures trends in wake centerline velocity deficit for 𝑆𝑡𝑓 = 0.12 and 0.25 but fails for 𝑆𝑡𝑓 =0.84 (in both wake centerline velocity deficit and position). The authors should discuss potential reasons for this discrepancy.
5. The current model is developed and validated only for a single turbine. While the results are promising, it remains unclear how the approach would capture the cumulative effects of multiple interacting turbine wakes in a wind farm. This limitation should be explicitly discussed in the manuscript.
6. I believe there is a need to make lines 30–35 on page 2 more accurate.
7. Please clarify the definition of the turbine operational parameter Cop?
8. Both the abstract and conclusion are highly qualitative. Including quantitative metrics on model accuracy would significantly improve the clarity and impact of the results.
9. Text in some sections seems repetitive, which disrupts readability. Streamlining text while keeping clarity is recommended.Minor comments:
- There are a few citation issues (e.g., repeated names such as “Jensen Jensen”) that should be corrected.
- Check Eq. (6): is it a complete equation or only a partial expression?
- Consider using a term other than “real” for LES predictions; “ground truth” is more accurate.
- Line 320, page 19, is unclear and needs clarification.Citation: https://doi.org/10.5194/wes-2025-189-RC2 - AC2: 'Reply on RC2', Xiaolei Yang, 11 Jan 2026
-
RC3: 'Comment on wes-2025-189', Anonymous Referee #3, 06 Dec 2025
- AC3: 'Reply on RC3', Xiaolei Yang, 11 Jan 2026
Status: closed
-
RC1: 'Comment on wes-2025-189', Anonymous Referee #1, 03 Nov 2025
The authors present PhyWakeNet, a physics-integrated machine learning framework for dynamic wind turbine wake modeling under aerodynamic force oscillations. The model decomposes the instantaneous velocity field into time-averaged, meandering, and small-scale turbulent components. The time-averaged wake is governed by mass and momentum conservation with an entrainment-based closure; wake meandering uses conditional GAN-reconstructed SPOD modes with a data-driven dynamical system; small-scale turbulence is generated via a CNN. The model is trained and validated using LES data of a single NREL 5 MW turbine under transverse force oscillations at various Strouhal numbers (St_F). It successfully captures frequency-dependent wake recovery, meandering amplitude, and turbulence statistics.
Major Concerns
- Lack of Multi-Turbine Validation and Wake Superposition Most analytical wake models fail precisely in wake interaction and superposition within wind farms — a critical practical challenge. Despite the stated motivation of "wake management in wind farms," all results are for a single turbine. No simulation or discussion addresses how PhyWakeNet handles partial wake overlap, merged wakes, or cumulative turbulence in arrays.
Why was no multi-turbine case investigated? This omission severely limits the claimed applicability. The authors should either:
- Include at least one 2–3 turbine inline or staggered case (with wake superposition), or
- Explicitly justify the single-turbine focus and discuss planned extensions to farm-scale modeling. Without this, the wind farm relevance remains speculative.
- Inadequate Literature Review on ML-Assisted Wake Modeling The core innovation is ML integration (CGAN + CNN + physics) for dynamic wake prediction — yet the introduction lacks any review of prior ML-based wake or turbulence modeling. Relevant works are not cited.
A dedicated paragraph is needed comparing:
- Data-driven vs. physics-constrained approaches
- SPOD + GAN vs. POD-RBF, LSTM, or PINN methods
- Quantitative performance (e.g., error in deficit, TKE, meandering) Without this context, the novelty and improvement over existing ML wake models are unclear.
- Figure Clarity and Completeness Issues
- Figure 13: The difference between red and gray lines is not explained in the caption or text.
- Figure 13(c,d): Horizontal axis labels are illegible (overlapping or cut off).
- Figure 9 and Figure 12: Captions state “five rows (a–e, f–j)” but subplots d, e, i, j are missing in the figures.
- Figure 11: No legend — unclear which line corresponds to LES, PhyWakeNet, or submodels (only mentioned in the caption).
These errors undermine result interpretation and must be corrected.
- Critical ML Methodology Relegated to Appendix In data-driven modeling, dataset generation, model architecture, training strategy, and validation protocol are core contributions. Currently:
- LES setup, SPOD extraction, CGAN/CNN architectures, loss functions, training data split, and validation metrics are buried in appendices.
- The main text jumps from equations to results with minimal explanation of how the ML models were built or validated.
Move key ML details to the main body, including:
- Table of LES cases (St_F, turbulence intensity, length scale)
- CGAN and CNN architectures (layers, inputs, conditioning)
- Training/validation split, loss functions, and convergence
- Number of SPOD modes (N) and sensitivity hyperparameter tuning may remain in appendix, but model design and data pipeline must be in the main paper.
- Minor but Important Typos and Inconsistencies
- Figure 1 caption: “GCAN” → should be CGAN.
Citation: https://doi.org/10.5194/wes-2025-189-RC1 - AC1: 'Reply on RC1', Xiaolei Yang, 11 Jan 2026
- Lack of Multi-Turbine Validation and Wake Superposition Most analytical wake models fail precisely in wake interaction and superposition within wind farms — a critical practical challenge. Despite the stated motivation of "wake management in wind farms," all results are for a single turbine. No simulation or discussion addresses how PhyWakeNet handles partial wake overlap, merged wakes, or cumulative turbulence in arrays.
-
RC2: 'Comment on wes-2025-189', Anonymous Referee #2, 06 Nov 2025
The manuscript presents a hybrid framework for developing a dynamic wake model that integrates first principles with machine learning (ML) techniques. The ultimate goal is to enable dynamic single-turbine wake modeling accounting for aerodynamic force oscillations. The authors leverage three sub-models to capture time-averaged wake, wake meandering, and small-scale wake turbulence. Some submodels are trained using LES data, and the results show generally good agreement with the ground truth. The work addresses an important problem in wind-energy modeling and has potential for impactful contributions. However, there are several points that need to be addressed to strengthen the manuscript.
Major comments:
1. A primary concern is that the ML models are mostly treated as "black box. There is no discussion or demonstration of explainability, such as feature importance or SHAP tools. Since two of the submodels rely heavily on ML and directly affect the first submodel and overall wake predictions, the lack of explainability limits the credibility and understanding of the framework. It is strongly recommended to include an assessment of how the ML predictions are derived and how dependent they are on inputs.
2. The manuscript lacks a comprehensive review of recent literature in data-driven wake modeling, especially regarding generalization and explainability of ML-based wake predictions. Providing a critical comparison would clarify the novelty of this work.
3. Please provide a quantified comparison of the onset of wake meandering rather than relying on qualitative assessment from the results in Figure 12.
4. Regarding Figure 14: I agree with the authors that the model struggles more in predicting the wake centerline velocity deficit than the wake center position. The model captures trends in wake centerline velocity deficit for 𝑆𝑡𝑓 = 0.12 and 0.25 but fails for 𝑆𝑡𝑓 =0.84 (in both wake centerline velocity deficit and position). The authors should discuss potential reasons for this discrepancy.
5. The current model is developed and validated only for a single turbine. While the results are promising, it remains unclear how the approach would capture the cumulative effects of multiple interacting turbine wakes in a wind farm. This limitation should be explicitly discussed in the manuscript.
6. I believe there is a need to make lines 30–35 on page 2 more accurate.
7. Please clarify the definition of the turbine operational parameter Cop?
8. Both the abstract and conclusion are highly qualitative. Including quantitative metrics on model accuracy would significantly improve the clarity and impact of the results.
9. Text in some sections seems repetitive, which disrupts readability. Streamlining text while keeping clarity is recommended.Minor comments:
- There are a few citation issues (e.g., repeated names such as “Jensen Jensen”) that should be corrected.
- Check Eq. (6): is it a complete equation or only a partial expression?
- Consider using a term other than “real” for LES predictions; “ground truth” is more accurate.
- Line 320, page 19, is unclear and needs clarification.Citation: https://doi.org/10.5194/wes-2025-189-RC2 - AC2: 'Reply on RC2', Xiaolei Yang, 11 Jan 2026
-
RC3: 'Comment on wes-2025-189', Anonymous Referee #3, 06 Dec 2025
- AC3: 'Reply on RC3', Xiaolei Yang, 11 Jan 2026
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The authors present PhyWakeNet, a physics-integrated machine learning framework for dynamic wind turbine wake modeling under aerodynamic force oscillations. The model decomposes the instantaneous velocity field into time-averaged, meandering, and small-scale turbulent components. The time-averaged wake is governed by mass and momentum conservation with an entrainment-based closure; wake meandering uses conditional GAN-reconstructed SPOD modes with a data-driven dynamical system; small-scale turbulence is generated via a CNN. The model is trained and validated using LES data of a single NREL 5 MW turbine under transverse force oscillations at various Strouhal numbers (St_F). It successfully captures frequency-dependent wake recovery, meandering amplitude, and turbulence statistics.
Major Concerns
Why was no multi-turbine case investigated? This omission severely limits the claimed applicability. The authors should either:
A dedicated paragraph is needed comparing:
These errors undermine result interpretation and must be corrected.
Move key ML details to the main body, including: