A Three-Dimensional Analytical Model for Wind Turbine Wakes from Near to Far Field: Incorporating Atmospheric Stability Effects

This study proposes and systematically validates a new analytical wake model that incorporates atmospheric stability effects. By introducing a stability-dependent turbulence expansion term with a square of a cosine function and the stability sign parameter, the model dynamically responds to varying atmospheric conditions, overcoming the reliance of tranditional models on neutral atmospheric assumptions. It achieves physically consistent descriptions of turbulence suppression under stable conditions and convective enhancement under unstable conditions. A newly developed far-field decay function effectively coordinates near-wake and far-wake evolution, maintaining computational efficiency while significantly improving prediction accuracy under complex stability conditions. The Present model has been validated against field measurements from the Scaled Wind Farm Technology (SWiFT) facility and the Alsvik wind farm, demonstrating superior performance in predicting wake velocity distributions on both vertical and horizontal planes. It also exhibits strong adaptability under neutral, stable, and unstable atmospheric conditions. This proposed framework provides a reliable tool for wind turbine layout optimization and power output forecasting under realistic atmospheric stability conditions.