Similarity functions and a new k−ε closure for predicting stratified atmospheric surface layer flows in complex terrain

Most of the k−ε closures for modeling stratified surface layer are derived from the classical similarity functions and might fail in complex terrain due to limitations of the classical similarity functions. Despite the classical similarity functions to limit the flux Richardson number Rf, we present new similarity functions estimated from field measurement in full range of Rf and propose a k−ε model using the new similarity functions to improve predictions of stratified surface layer flows in complex terrain. Measurements show that the classical similarity functions are partially valid in complex terrain and the wind shear under strongly stable conditions is constrained at large Rf. According to numerical studies in two areas of complex terrain, models using the classical similarity functions and the new similarity functions both present good predictions of convective airflows in complex terrain. The new similarity functions are shown to significantly improve the k−ε model in predicting stably stratified airflows in complex terrain by constraining the wind shear at large Rf, while the classical similarity functions without limiting the wind shear lead to significantly misestimating the wind speedup factor under stable conditions. Using the proposed model to predict flows in wind farm could benefit wind resource estimation and wind power forecasting.