Large-eddy simulation of wind turbine wake dynamics over steep hilly terrain: Effects of terrain-to-turbine scale ratio and surface roughness

Understanding and predicting the coupling effect of turbine wakes, atmospheric winds, and local topographically induced flows is crucial for the deployment of a mountainous wind farm. This study systematically investigates the wake dynamics of a wind turbine installed atop steep hilly terrain using large eddy simulations, particularly considering the effects of terrain-to-turbine scale ratio and surface roughness. The results reveal that increasing the terrain-to-turbine scale ratio and surface roughness accelerates wake recovery, while the wake deflection is jointly influenced by topography-induced flow disturbances and Coriolis effects. The added turbulence intensity in the near wake downstream of the upper and lower rotor tips is elevated as the terrain-to-turbine scale ratio increases and surface roughness decreases. Moreover, the peak frequency of streamwise velocity spectra shifts downstream from near- to far-wake due to enhanced turbulent mixing and wake-hill interaction, with greater reductions observed under higher terrain-to-turbine scale ratios and surface roughness. Compared to flat terrain, hilly terrain enhances sweep and ejection motions at the lower-tip height and suppresses them at the upper-tip height in the near wake region, while the quadrant-based Reynolds stress contributions are negligibly affected by terrain or surface roughness with the wake developing downstream. This study advances physical understanding of wake–terrain interactions and provides practical implications for wind turbine and wind farm design over complex terrain, with emphasis on the influence of turbine-to-terrain scale ratio and surface roughness.