The impact of the atmospheric boundary layer on the asymmetric wake profile: A bivariate analysis

Abstract

The complexities of wind turbine wake evolution necessitate the estimation of turbulence and horizontal and vertical wake expansion. The standard approach for developing a Gaussian wake model based on Gaussian similarity assumes that the turbine wake profile is symmetric around the hub height and approximates a normal distribution. The impacts of Atmospheric Boundary Layer (ABL) and ground surface roughness cause the wake to deviate from radial symmetry, resulting in a nonsymmetric wake around hub height. We develop the Bivariate Gaussian (B-Gaussian) Model to estimate the nonsymmetrical wind turbine wake expansion due to ABL effects. The B-Gaussian model factors the correlation coefficient (Ω) to compare the horizontal and vertical expansions. The radial profiles result for the B-Gaussian shows a faster wake decay for the unstable ABL because of faster mixing at higher-turbulence intensities, and slower wake decay is due to slower mixing at lower-turbulence intensities for the stable ABL. The radial wake profiles for the unstable ABL transition from vertical elliptical-shaped in the near wake region to double circular-shaped profiles in the far-wake region as Ω decreases. Finally, compared to preceding Gaussian models, the B-Gaussian outperforms previous Gaussian wake models and has the least overall and downstream entrainment errors.