Secondary flows in the actuator-disk simulation of wind-turbine wakes

This study explores the generation of secondary flows of Prandtl's second kind in the actuator-disk simulation of wind-turbine wakes. Leveraging large-eddy simulation data and conducting an analysis of the mean streamwise vorticity budget, we uncover the physical mechanisms contributing to this phenomenon. Our investigations attribute the emergence of such flows to the spatial gradients of the Reynolds stresses in the wake downstream of the turbines, which are, in turn, influenced by ground effects. To further investigate the phenomenon, we specifically isolate the impact of secondary flows on the wake by employing a model recognized for its incapacity to capture such dynamics: a two-equation Reynolds-averaged Navier-Stokes (RANS) model founded on the linear eddy-viscosity hypothesis. By comparing the predictions of the RANS model with those of large-eddy simulations and wind-tunnel experiments, we highlight the effect of secondary flows on the wake structure and, in particular, the upward shift of the wake. Motivated by the obtained results, we then enhance the baseline RANS model by introducing a non-linear term within the Reynolds stress tensor. This modification leads to a more accurate representation of Reynolds stresses, enabling the RANS model to capture the secondary flows in the wake. Our analysis emphasizes the importance of employing advanced RANS models in the simulation of wind farms.