Analytical coupled Ekman and surface layer model for ABL flows and applications to wind farm modeling*

We propose a physics-based analytical model for predicting wind velocities in conventionally neutral and stable atmospheric boundary layer (ABL) flows. Unlike traditional approaches like the Monin-Obukhov Similarity Theory, which focuses solely on modeling profiles of wind magnitude within the surface layer, our model offers improved predictions of both streamwise and wind veer velocity profiles across varying atmospheric conditions throughout the entire ABL height. The model also provides estimates of friction velocity and geostrophic wind velocities using a new self-consistent geostrophic drag law (GDL) that is derived by matching velocities in the inner and outer layers. To validate our model, we compare model results with Large Eddy Simulation (LES) data. The results demonstrate very good agreement over a wide range of stability conditions. Furthermore, we integrate the analytical velocity profiles into wind turbine wake models to effectively account for sheared wake structures resulting from wind veer in a thermally stably stratified ABL. We present comparisons of this enhanced analytical wake model with LES results.