A linear wake expansion function for the double-Gaussian analytical wake model

The double-Gaussian (DG) approach for analytical wake modeling leads to a better understanding of the wake transition mechanism within a full-wake region behind a non-yawed horizontal-axis wind turbine (HAWT). To date, a key parameter of the wake expansion in the DG model still has yet to be defined explicitly instead of tuning, thus limiting its usability for practical applications. The present work aims to overcome this limitation by proposing a simple linear wake expansion function for the DG model constructed from the existing parameters based on the conservation of mass and momentum. Considering the physical and statistical approaches, the proposed function is specifically intended to approximate the wake expansion downstream of a non-yawed HAWT under turbulence inflow. Seven case studies from wind tunnel measurements and large eddy simulations under different inflow conditions were used to examine the effectiveness of the proposed function. In general, the evaluation results in the present study show the effectiveness of the proposed expansion function for the DG wake model to predict the wake expansion and its recovery behind a non-yawed HAWT without a prior adjustment or tuning of the wake expansion parameter.