Theoretical efficiency of a wind turbine in non-uniform base flow: Revisiting the Betz–Joukowsky limit

Classical one-dimensional momentum theory suggests that there is an upper limit to the power that can be extracted from the available wind resource. In the present work, we relax the assumption of constant velocity and investigate how the power efficiency of a turbine is affected by a non-uniform velocity field in the base flow. The analysis shows that a non-uniform base flow velocity in the streamwise direction can increase or decrease the maximum theoretical efficiency of a turbine for accelerating or decelerating flow, respectively. Furthermore, the effect of cross-stream flow shear on the maximum theoretical efficiency of a turbine is discussed.