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Generation and decay of counter-rotating vortices downstream of yawed wind turbines in the atmospheric boundary layer

Published online by Cambridge University Press:  22 September 2020

Carl R. Shapiro Open the ORCID record for Carl R. Shapiro [Opens in a new window] ,
Dennice F. Gayme Open the ORCID record for Dennice F. Gayme [Opens in a new window]  and
Charles Meneveau Open the ORCID record for Charles Meneveau [Opens in a new window]
Carl R. Shapiro*
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD21218, USA
Dennice F. Gayme
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD21218, USA
Charles Meneveau
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD21218, USA
*
†Email address for correspondence: cshapir5@jhu.edu
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Abstract

A quantitative understanding of the dominant mechanisms that govern the generation and decay of the counter-rotating vortex pair (CVP) produced by yawed wind turbines is needed to fully realize the potential of yawing for wind farm power maximization and regulation. Observations from large eddy simulations (LES) of yawed wind turbines in the turbulent atmospheric boundary layer and concepts from the aircraft trailing vortex literature inform a model for the shed vorticity and circulation. The model is formed through analytical integration of simplified forms of the vorticity transport equation. Based on an eddy viscosity approach, it uses the boundary-layer friction velocity as the velocity scale and the width of the vorticity distribution itself as the length scale. As with the widely used Jensen model for wake deficit evolution in wind farms, our analytical expressions do not require costly numerical integration of differential equations. The predicted downstream decay of maximum vorticity and total circulation agree well with LES results. We also show that the vorticity length scale grows linearly with downstream distance and find several power laws for the decay of maximum vorticity. These results support the notion that the decay of the CVP is dominated by gradual cancellation of the vorticity at the line of symmetry of the wake through cross-diffusion.

JFM classification

Turbulent Flows: Turbulent boundary layers Wakes/Jets: Wakes Vortex Flows: Vortex dynamics

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Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 903 , 25 November 2020 , R2
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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