Physics-based modelling of turbulence in wind-turbine wakes

So-called engineering or analytical wind farm flow solvers typically build upon two submodels: one for the velocity deficit and one for the wake-added turbulence intensity. While velocity deficit modelling has received considerable attention, wake-added turbulence models are less prevalent in comparison. Yet, accurate estimates of local turbulence intensity are essential for predicting flow interactions and energy yield, as turbine wakes are both sensitive to and sources of turbulence. Existing wake-added turbulence models are typically empirical or assume axial symmetry despite the inherently three-dimensional nature of turbulent wake fields. In this work, we present a physics-based model for wake-added turbulence intensity. Our approach is based on the analysis of the turbulent kinetic energy and the streamwise Reynolds stress budget, incorporating classical RANS modelling assumptions and far-wake approximations. The resulting model maintains a simple and practical form, demonstrating strong agreement with LES and wind tunnel measurements. Our model provides a more physically consistent and predictive tool for wind farm flow modelling and performance estimation.