An extended analytical wake model and applications to yawed wind turbines in atmospheric boundary layers with different levels of stratification and veer

Abstract

Analytical wake models provide a computationally efficient means to predict velocity distributions in wind turbine wakes in the atmospheric boundary layer (ABL). Most existing models are developed for neutral atmospheric conditions and correspondingly neglect the effects of buoyancy and Coriolis forces that lead to veer, i.e. changes in the wind direction with height. Both veer and changes in thermal stratification lead to lateral shearing of the wake behind a wind turbine, which affects the power output of downstream turbines. Here we develop an analytical engineering wake model for a wind turbine in yaw in ABL flows including Coriolis and thermal stratification effects. The model combines the new analytical representation of ABL vertical structure based on coupling Ekman and surface layer descriptions (Narasimhan, Gayme, and Meneveau, 2024a) with the vortex sheet-based wake model for yawed turbines (Bastankhah et al., 2022), as well as a new method to predict the wake expansion rate based on the Townsend-Perry logarithmic scaling of streamwise velocity variance. The proposed wake model's predictions show good agreement with Large Eddy Simulation (LES) results, capturing the effects of wind veer and yawing including the curled and sheared wake structures across various states of the ABL, ranging from neutrally to strongly stably stratified atmospheric conditions. The model significantly improves power loss predictions from wake interactions, especially in strongly stably stratified conditions where wind veer effects dominate.