Analytical modeling of wind-turbine wakes behind an abrupt rough-to-smooth surface roughness transition

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Numerous wind farms are planned and built in the coastal or forest-to-grassland transition areas with abrupt rough-to-smooth surface roughness change. Behind the abrupt change, the atmospheric boundary layer (ABL) undergoes a complex transition process which brings big challenges to the canonical wake models of wind turbines. To this end, we employ large eddy simulation (LES) to investigate the development of the ABL and the evolution of wind-turbine wakes at different positions under roughness abruption from rough to smooth, and propose a novel analytical wake model. Due to the abrupt change of surface roughness, pressure gradient forms around the abruption and the internal boundary layer (IBL) develops downstream. The wind turbine near the abruption point is influenced by the pressure gradient, resulting in smaller wake width, while those situated within the IBL are significantly affected by the flow transition, resulting in systematic differences in wake recovery. To explicitly account for the flow transition in the wake model, we introduce an equivalent additional thrust to represent the momentum contribution caused by both background velocity and Reynolds stress. A detailed budget analysis is then conducted around the wind turbine and shows that the equivalent additional thrust is highly correlated with the streamwise turbulence intensity. Finally, a new wake model under roughness abruption is developed and compared with the LES data. Results show that the proposed model demonstrates superior performance over the existing models.