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Evolution and instability of the tip vortices behind a yawed wind turbine

Published online by Cambridge University Press:  30 July 2025

Chao Li Open the ORCID record for Chao Li [Opens in a new window] ,
An-Kang Gao Open the ORCID record for An-Kang Gao [Opens in a new window] ,
Luoqin Liu Open the ORCID record for Luoqin Liu [Opens in a new window] ,
Xi-Yun Lu Open the ORCID record for Xi-Yun Lu [Opens in a new window]  and
Richard J.A.M. Stevens Open the ORCID record for Richard J.A.M. Stevens [Opens in a new window]
Chao Li
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, PR China
An-Kang Gao
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, PR China
Luoqin Liu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, PR China
Xi-Yun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, PR China
Richard J.A.M. Stevens
Affiliation:
Physics of Fluids Group, Max Planck Center Twente for Complex Fluid Dynamics, J.M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, Enschede, 7500 AE, The Netherlands
*
Corresponding author: Luoqin Liu, luoqinliu@ustc.edu.cn
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Abstract

Yaw control can effectively enhance wind farm power output, but the vorticity distribution and coherent structures in yawed turbine wakes remain poorly understood. We propose a physical model capable of accurately predicting tip vortex dynamics from their generation to destabilisation. This model integrates a point vortex framework with advanced blade element momentum theory and vortex cylinder theory for yawed turbines. Comparisons with large eddy simulations demonstrate that the model effectively predicts the vorticity distribution of tip vortices and the wake profile of yawed turbines. Finally, we employ sparsity-promoting dynamic mode decomposition to analyse the dynamics of the far wake. Our analysis reveals four primary mode types: (i) the averaged mode; (ii) shear modes; (iii) harmonic modes; and (iv) merging modes. Under yawed conditions, these modes become asymmetric, leading to interactions between the tip and root vortex modes. This direct interaction plays a critical role during the formation process of the counter-rotating vortex pair observed in yawed wakes.

JFM classification

Instability: Instability Vortex Flows: Vortex dynamics Wakes/Jets: Wakes

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JFM Papers
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Journal of Fluid Mechanics , Volume 1016 , 10 August 2025 , A20
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© The Author(s), 2025. Published by Cambridge University Press

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