Physics-based and stability-aware analytical modeling of wind turbine wakes

Wind turbine wake behavior is strongly affected by atmospheric stability, yet most analytical wake models have been developed and validated under neutral boundary-layer conditions. As a result, their predictive reliability under stable and convective stratification remains uncertain. In this study, we address this gap by evaluating the physics-based wake-expansion model of Vahidi and Porté-Agel (2022) (VPA model) using large-eddy simulation (LES) data spanning stable, neutral, and convective atmospheric boundary layers. The model shows consistently strong agreement with LES across all stability regimes, with root-mean-square wake-deficit errors below 5%. A key contribution of this work is the assessment of the VPA model robustness when Lagrangian integral time scales—quantities rarely available in field measurements—are replaced by empirical estimates. The results demonstrate low sensitivity to uncertainties in these inputs, indicating that accurate wake predictions can be achieved using turbulence quantities obtainable, in principle, from high-frequency velocity measurements. Importantly, the VPA model links wake expansion to cross-stream turbulence intensities and integral time scales, which control lateral and vertical wake meandering and mixing, unlike classical Gaussian formulations that rely solely on the streamwise turbulence intensity. Guided by physical insights from the validated model, we propose a simple stability-aware refinement of the classical Gaussian wake formulation, linking the total wake-growth rate to the radial turbulence intensity. This refinement improves wake predictions under non-neutral conditions while preserving analytical simplicity, making it suitable for wind-energy engineering applications.