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

In response to the critical demand for improved characterization of atmospheric stability effects in wind turbine wake prediction, this study proposes and systematically validates a new analytical wake model that incorporates atmospheric stability effects. In recent years, research on wake models with atmospheric stability effects has primarily followed two approaches: incorporating stability through high-fidelity numerical simulations or modifying classical analytical wake models. While the former offers clear mechanical insights, it incurs high computational costs, whereas the latter improves efficiency yet often suffers from near-wake prediction biases under stable stratification, lacks a unified framework covering the entire wake region, and relies heavily on case-specific calibration of key parameters. To overcome these limitations, this study introduces a stability-dependent turbulence expansion term with a square of a cosine function and the stability sign parameter, enabling the model to dynamically respond to varying atmospheric conditions and overcome the reliance of traditional 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.