Wind Turbine Wakes Under Different Atmospheric Conditions: Bridging Internal Dynamics and Meandering with Taylor’s Diffusion Theory

Abstract Atmospheric conditions influence wind turbine wake behavior, which in turn affects power production and structural loads. Two major aspects of this impact are wake meandering and wake expansion. Taylor’s diffusion theory, originally developed for particle dispersion, has been used to describe the dispersion of the wake structure center, although it is not a particle. The present study proposes a framework that bridges Taylor’s diffusion theory from wake particles to the wake structure center by describing the wake structure as a surface-averaged entity of particle positions. Thus, the applicability of Taylor’s diffusion theory to describe wake diffusion processes, such as wake meandering and wake expansion, is established. Additionally, an extended version of the theory is proposed to more accurately represent wake expansion. Large Eddy Simulations (LES) are conducted using the Meso-NH solver for three atmospheric stability conditions: stable, neutral, and unstable. To validate theoretical predictions, two distinct wake tracking methodologies are employed: Eulerian and Lagrangian. The results demonstrate that wake meandering is driven by the Eulerian turbulent time scale of the upstream flow, while wake expansion is governed by the Lagrangian turbulent time scale, along with internal dynamics described by mixing layer theory. The significance of this study lies in its conceptualisation of wake diffusion processes as a unifying theoretical framework, emphasising the necessity of understanding the turbulent structure of the upstream flows to enhance the predictive capabilities of wind turbine wakes across a variety of atmospheric conditions.