Coupled effects of atmospheric stability and terrain slope on wind turbine wake evolution and downstream power performance over hilly terrain

The rapid deployment of onshore wind farms in complex terrain is an important pathway for expanding wind energy deployment. However, the coupled effects of atmospheric stability and terrain slope on wind turbine wake evolution and downstream power performance remain insufficiently understood, hindering accurate energy-yield assessment and effective wind-farm layout optimization. In this study, high-fidelity large-eddy simulations are conducted to investigate turbine wakes over flat terrain, a gentle hill, and a steep hill under convective, neutral, and stable atmospheric conditions. The results demonstrate that wake evolution and downstream power performance are jointly controlled by atmospheric stability, terrain slope, and upstream turbine wakes. Coriolis-induced wind veer and terrain-induced flow distortion lead to three-dimensional wake deflection, which becomes more pronounced with increasing atmospheric stability and terrain slope. Under stable conditions over the steep hill, the downstream distributions of power loss and power variability exhibit pronounced asymmetry, together with faster power recovery. Momentum-flux analysis shows that this accelerated recovery is primarily driven by downward mean advective transport from the low-level jet rather than by enhanced turbulent mixing. Terrain-induced power loss and variability increase with terrain slope because of intensified flow separation on the leeward side. In contrast, the power loss and variability caused by upstream turbine wakes decrease over steeper terrain because the increased elevation difference reduces direct wake impingement on the downstream rotor. These findings clarify the coupled terrain–stability mechanisms governing wind turbine wakes and provide guidance for energy-yield assessment and turbine layout optimization in complex terrain.