Articles | Volume 8, issue 3
https://doi.org/10.5194/wes-8-401-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/wes-8-401-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
24 Mar 2023
Research article |
| 24 Mar 2023
| 24 Mar 2023
Addressing deep array effects and impacts to wake steering with the cumulative-curl wake model
Christopher J. Bay
CORRESPONDING AUTHOR
National Wind Technology Center, National Renewable Energy Laboratory, Golden, CO 80401, USA
Paul Fleming
National Wind Technology Center, National Renewable Energy Laboratory, Golden, CO 80401, USA
Bart Doekemeijer
National Wind Technology Center, National Renewable Energy Laboratory, Golden, CO 80401, USA
Jennifer King
National Wind Technology Center, National Renewable Energy Laboratory, Golden, CO 80401, USA
Matt Churchfield
National Wind Technology Center, National Renewable Energy Laboratory, Golden, CO 80401, USA
Rafael Mudafort
National Wind Technology Center, National Renewable Energy Laboratory, Golden, CO 80401, USA
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Cited
33 citations as recorded by crossref.
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- A Multi-Objective Optimization Framework for Offshore Wind Farm Design in Deep Water Seas V. Barnabei et al. https://doi.org/10.1115/1.4067365
- Toward ultra-efficient high-fidelity predictions of wind turbine wakes: Augmenting the accuracy of engineering models with machine learning C. Santoni et al. https://doi.org/10.1063/5.0213321
- A tuneable analytical wake model for offshore wind farms: bridging Jensen simplicity and CFD accuracy G. Navarro Diaz et al. https://doi.org/10.1088/1742-6596/3224/3/032062
- Prediction of multiple-wake velocity and wind power using a cosine-shaped wake model Z. Zhang & P. Huang https://doi.org/10.1016/j.renene.2023.119418
- A new physically based model for cumulative wakes and application to wind farms Z. Zhang et al. https://doi.org/10.1016/j.enconman.2026.121593
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- Artificial intelligence-aided wind plant optimization for nationwide evaluation of land use and economic benefits of wake steering D. Harrison-Atlas et al. https://doi.org/10.1038/s41560-024-01516-8
- Benchmarking engineering wake models for farm-to-farm interactions L. Vollmer et al. https://doi.org/10.1088/1742-6596/2767/9/092095
- Evaluation of wake superposition methods for wind-farm flow and power prediction B. Du et al. https://doi.org/10.1088/1742-6596/3016/1/012036
- Advancements in Wind Farm Control: Modelling and Multi-Objective Optimization Through Yaw-Based Wake Steering T. Lucas Frutuoso et al. https://doi.org/10.3390/en18092247
- Numerical modelling of offshore wind-farm cluster wakes P. Ouro et al. https://doi.org/10.1016/j.rser.2025.115526
- A new analytical wake model with application to power prediction Z. Zhang & Q. Li https://doi.org/10.1016/j.oceaneng.2026.126981
- Comparison of steady-state analytical wake models implemented in wind farm analysis software R. Mudafort et al. https://doi.org/10.1088/1742-6596/2767/5/052066
- Modeling of Blockage and Wake Effect: Comparison with Field data P. Maheshwari et al. https://doi.org/10.1088/1742-6596/2767/9/092021
- A momentum-conserving wake superposition method for wind-farm flows under pressure gradient B. Du et al. https://doi.org/10.1017/jfm.2024.761
- Ranking multi-fidelity model performances in reproducing internal and external wake impacts at neighbouring offshore wind farms S. Freitas et al. https://doi.org/10.1088/1742-6596/2767/9/092045
- Design-friendly wind farm control setpoint estimation via layout-agnostic graph neural networks D. Dirik et al. https://doi.org/10.1088/1742-6596/3224/3/032112
- Wind farm layout optimization using a novel machine learning approach M. Gholami Anjiraki et al. https://doi.org/10.1063/5.0326424
- Scalable SCADA-Based Calibration for Analytical Wake Models Across an Offshore Cluster D. Binsbergen et al. https://doi.org/10.1088/1742-6596/2745/1/012014
- Risk-averse wake steering optimization for energy and power maximization under uncertain wind direction changes M. Becker & J. Wingerden https://doi.org/10.1088/1742-6596/3224/3/032124
- A dynamic open-source model to investigate wake dynamics in response to wind farm flow control strategies M. Becker et al. https://doi.org/10.5194/wes-10-1055-2025
- Integrated wind farm design: optimizing turbine placement and cable routing with wake effects J. Pedersen et al. https://doi.org/10.1007/s00291-026-00862-1
- Analytical modelling of wind-turbine wake turbulence in neutral atmospheric boundary layers F. Blondel et al. https://doi.org/10.1017/jfm.2026.11685
- Hyperparameter tuning framework for calibrating analytical wake models using SCADA data of an offshore wind farm D. van Binsbergen et al. https://doi.org/10.5194/wes-9-1507-2024
- Validation of an interpretable data-driven wake model using lidar measurements from a field wake steering experiment B. Sengers et al. https://doi.org/10.5194/wes-8-747-2023
- Gaussian FLOWERS: Wind-rose-based analytical integration of Gaussian wake model for extremely fast AEP estimation C. Whittaker et al. https://doi.org/10.1063/5.0245886
- Optimal wind farm energy and reserve scheduling incorporating wake interactions M. Mabboux-Fort et al. https://doi.org/10.1016/j.apenergy.2026.127815
- A Comparative Analysis of Actuator-Based Turbine Structure Parametrizations for High-Fidelity Modeling of Utility-Scale Wind Turbines under Neutral Atmospheric Conditions C. Santoni et al. https://doi.org/10.3390/en17030753
- Multi-model approach for wind resource assessment B. Sengers et al. https://doi.org/10.1088/1742-6596/2767/9/092024
- Energy Storage and Management of Offshore Wind-Based Green Hydrogen Production I. Pizzuti et al. https://doi.org/10.3390/pr13030643
- A fast-running physics-based wake model for a semi-infinite wind farm M. Bastankhah et al. https://doi.org/10.1017/jfm.2024.282
- Wind pattern clustering of high frequent field measurements for dynamic wind farm flow control M. Becker et al. https://doi.org/10.1088/1742-6596/2767/3/032028
33 citations as recorded by crossref.
- Augmenting Offshore Wind-Farm Yield with Tethered Kites K. Zammit et al. https://doi.org/10.3390/en19030668
- A Multi-Objective Optimization Framework for Offshore Wind Farm Design in Deep Water Seas V. Barnabei et al. https://doi.org/10.1115/1.4067365
- Toward ultra-efficient high-fidelity predictions of wind turbine wakes: Augmenting the accuracy of engineering models with machine learning C. Santoni et al. https://doi.org/10.1063/5.0213321
- A tuneable analytical wake model for offshore wind farms: bridging Jensen simplicity and CFD accuracy G. Navarro Diaz et al. https://doi.org/10.1088/1742-6596/3224/3/032062
- Prediction of multiple-wake velocity and wind power using a cosine-shaped wake model Z. Zhang & P. Huang https://doi.org/10.1016/j.renene.2023.119418
- A new physically based model for cumulative wakes and application to wind farms Z. Zhang et al. https://doi.org/10.1016/j.enconman.2026.121593
- Integer programming for optimal yaw control of wind farms F. Bestehorn et al. https://doi.org/10.5194/wes-10-1637-2025
- Artificial intelligence-aided wind plant optimization for nationwide evaluation of land use and economic benefits of wake steering D. Harrison-Atlas et al. https://doi.org/10.1038/s41560-024-01516-8
- Benchmarking engineering wake models for farm-to-farm interactions L. Vollmer et al. https://doi.org/10.1088/1742-6596/2767/9/092095
- Evaluation of wake superposition methods for wind-farm flow and power prediction B. Du et al. https://doi.org/10.1088/1742-6596/3016/1/012036
- Advancements in Wind Farm Control: Modelling and Multi-Objective Optimization Through Yaw-Based Wake Steering T. Lucas Frutuoso et al. https://doi.org/10.3390/en18092247
- Numerical modelling of offshore wind-farm cluster wakes P. Ouro et al. https://doi.org/10.1016/j.rser.2025.115526
- A new analytical wake model with application to power prediction Z. Zhang & Q. Li https://doi.org/10.1016/j.oceaneng.2026.126981
- Comparison of steady-state analytical wake models implemented in wind farm analysis software R. Mudafort et al. https://doi.org/10.1088/1742-6596/2767/5/052066
- Modeling of Blockage and Wake Effect: Comparison with Field data P. Maheshwari et al. https://doi.org/10.1088/1742-6596/2767/9/092021
- A momentum-conserving wake superposition method for wind-farm flows under pressure gradient B. Du et al. https://doi.org/10.1017/jfm.2024.761
- Ranking multi-fidelity model performances in reproducing internal and external wake impacts at neighbouring offshore wind farms S. Freitas et al. https://doi.org/10.1088/1742-6596/2767/9/092045
- Design-friendly wind farm control setpoint estimation via layout-agnostic graph neural networks D. Dirik et al. https://doi.org/10.1088/1742-6596/3224/3/032112
- Wind farm layout optimization using a novel machine learning approach M. Gholami Anjiraki et al. https://doi.org/10.1063/5.0326424
- Scalable SCADA-Based Calibration for Analytical Wake Models Across an Offshore Cluster D. Binsbergen et al. https://doi.org/10.1088/1742-6596/2745/1/012014
- Risk-averse wake steering optimization for energy and power maximization under uncertain wind direction changes M. Becker & J. Wingerden https://doi.org/10.1088/1742-6596/3224/3/032124
- A dynamic open-source model to investigate wake dynamics in response to wind farm flow control strategies M. Becker et al. https://doi.org/10.5194/wes-10-1055-2025
- Integrated wind farm design: optimizing turbine placement and cable routing with wake effects J. Pedersen et al. https://doi.org/10.1007/s00291-026-00862-1
- Analytical modelling of wind-turbine wake turbulence in neutral atmospheric boundary layers F. Blondel et al. https://doi.org/10.1017/jfm.2026.11685
- Hyperparameter tuning framework for calibrating analytical wake models using SCADA data of an offshore wind farm D. van Binsbergen et al. https://doi.org/10.5194/wes-9-1507-2024
- Validation of an interpretable data-driven wake model using lidar measurements from a field wake steering experiment B. Sengers et al. https://doi.org/10.5194/wes-8-747-2023
- Gaussian FLOWERS: Wind-rose-based analytical integration of Gaussian wake model for extremely fast AEP estimation C. Whittaker et al. https://doi.org/10.1063/5.0245886
- Optimal wind farm energy and reserve scheduling incorporating wake interactions M. Mabboux-Fort et al. https://doi.org/10.1016/j.apenergy.2026.127815
- A Comparative Analysis of Actuator-Based Turbine Structure Parametrizations for High-Fidelity Modeling of Utility-Scale Wind Turbines under Neutral Atmospheric Conditions C. Santoni et al. https://doi.org/10.3390/en17030753
- Multi-model approach for wind resource assessment B. Sengers et al. https://doi.org/10.1088/1742-6596/2767/9/092024
- Energy Storage and Management of Offshore Wind-Based Green Hydrogen Production I. Pizzuti et al. https://doi.org/10.3390/pr13030643
- A fast-running physics-based wake model for a semi-infinite wind farm M. Bastankhah et al. https://doi.org/10.1017/jfm.2024.282
- Wind pattern clustering of high frequent field measurements for dynamic wind farm flow control M. Becker et al. https://doi.org/10.1088/1742-6596/2767/3/032028
Saved (final revised paper)
Latest update: 21 Aug 2026
Short summary
This paper introduces the cumulative-curl wake model that allows for the fast and accurate prediction of wind farm energy production wake interactions. The cumulative-curl model expands several existing wake models to make the simulation of farms more accurate and is implemented in a computationally efficient manner such that it can be used for wind farm layout design and controller development. The model is validated against high-fidelity simulations and data from physical wind farms.
This paper introduces the cumulative-curl wake model that allows for the fast and accurate...
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