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A vortex sheet based analytical model of the curled wake behind yawed wind turbines

Bastankhah, Majid and Shapiro, Carl R. and Shamsoddin, Sina and Gayme, Dennice F. and Meneveau, Charles (2021) 'A vortex sheet based analytical model of the curled wake behind yawed wind turbines.', Journal of Fluid Mechanics .


Motivated by the need for compact descriptions of the evolution of non-classical wakes behind yawed wind turbines, we develop an analytical model to predict the shape of curled wakes. Interest in such modelling arises due to the potential of wake steering as a strategy for mitigating power reduction and unsteady loading of downstream turbines in wind farms. We first estimate the distribution of the shed vorticity at the wake edge due to both yaw offset and rotating blades. By considering the wake edge as an ideally thin vortex sheet, we describe its evolution in time moving with the flow. Vortex sheet equations are solved using a power series expansion method, and an approximate solution for the wake shape is obtained. The vortex sheet time evolution is then mapped into a spatial evolution by using a convection velocity. Apart from the wake shape, the lateral deflection of the wake including ground effects is modelled. Our results show that there exists a universal solution for the shape of curled wakes if suitable dimensionless variables are employed. For the case of turbulent boundary layer inflow, the decay of vortex sheet circulation due to turbulent diffusion is included. Finally, we modify the Gaussian wake model by incorporating the predicted shape and deflection of the curled wake, so that we can calculate the wake profiles behind yawed turbines. Model predictions are validated against large-eddy simulations and laboratory experiments for turbines with various operating conditions.

Item Type:Article
Full text:Publisher-imposed embargo
(AM) Accepted Manuscript
File format - PDF
Publisher Web site:
Date accepted:01 November 2021
Date deposited:03 November 2021
Date of first online publication:2021
Date first made open access:No date available

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