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

TL;DR

This paper introduces a fully analytical wind turbine wake model that accounts for atmospheric stratification by using measurable turbulence properties, validated against simulations and outperforming existing models especially in unstable conditions.

Contribution

The model is the first to predict wake deficits solely from physical turbulence parameters without empirical tuning, improving accuracy across different atmospheric stratifications.

Findings

Excellent agreement with LES simulations across conditions

Superior performance over existing models in unstable atmospheres

Robustness to uncertainties in turbulence measurements

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.