A purely analytical and physical wind turbine wake model accounting for atmospheric stratification

Abstract

A purely analytical wake model for wind turbines is derived, anchored exclusively in physical interactions between atmospheric turbulence and turbine dynamics, and thus inherently accounting for atmospheric stratification. Unlike empirical models relying on assumed wake deficit shapes or tunable coefficients, this model predicts the wake deficit solely from measurable properties of the inflow, namely, turbulence intensity and the turbulence integral time scale. Systematic validation against Large Eddy Simulations (LES) for both IEA 15MW and NREL 5MW turbines, simulated in Meso-NH under stable, neutral, and unstable conditions, demonstrates excellent agreement across atmospheric regimes. Importantly, the model requires these specific turbulence statistics as input but shows only weak sensitivity to the integral time scale, ensuring robustness even with moderate uncertainties in inflow characterisation. Comparative analysis with the state-of-the-art Super-Gaussian analytical model highlights superior performance of the present approach, particularly for unstable and neutral stratification. These results show that the predictive accuracy gained by incorporating richer inflow physics justifies the need for more comprehensive atmospheric inputs, providing a clear pathway for physically grounded, calibration-free wake modeling in operational wind energy contexts.