Dependence of wind-farm-induced gravity waves and wind farm performance on non-dimensional atmospheric parameters and simulation configuration

Abstract

This large-eddy simulation (LES) study examines how wind-farm-induced atmospheric gravity waves (AGWs) and wind farm performance depend on non-dimensional atmospheric parameters and simulation configuration. A hypothetical aligned wind farm of actuator disks is simulated under neutral surface conditions, with a stable capping inversion and a mildly stable free atmosphere, to assess the effects of stratification beyond the atmospheric boundary layer (ABL) on ABL flow. Simulation set-ups fully resolving AGWs are validated to minimize spurious wave generation and reflection from the domain boundaries. The validated set-up is then used to analyze AGW types and characteristics, as well as stratification impacts under conventionally neutral boundary layer (CNBL) conditions. These conditions are governed by four non-dimensional parameters: the Froude numbers of the free atmosphere and capping inversion (Fr, F_ri), and the aspect ratios of the ABL and wind farm (_{H̃i Sh}). Simulation configurations that fully resolve AGWs-capturing at least one wavelength both horizontally and vertically-yield the most realistic stratification effects on ABL flow, whereas partial or unresolved configurations produce non-physical, channel-like behavior. A coherent description of the AGW phenomena is provided, highlighting the central role of capping inversion displacement in linking ABL fluctuations with AGWs. Trapped waves are confined within the capping inversion, while interfacial and internal waves aloft are identified as the AGW types most relevant to wind farm performance. The wavy inversion, analogous to an interfacial wave, forms converging and diverging zones that drive power fluctuations across the farm. The interfacial wavelength, measured over the wind farm, corresponds to one diverging, one converging, and one mildly diverging zone. As the interfacial wavelength decreases with F_ri, multiple convergence–divergence zones develop under sub-critical conditions (F_ri<1.0), while for super-critical conditions (F_ri>1.0), the wavelength approaches the farm length. Wave amplitude increases with decreasing _H̃i (i.e., shallower capping inversions). Wind farm performance is most sensitive to _H̃i: shallow boundary layers increase blockage and reduce efficiency, while deeper layers enhance efficiency. Increasing Fr and F_ri mitigates blockage, and increasing _Sh mainly improves wake recovery. Although local power fluctuations arise from AGWs, overall wind farm efficiency remains nearly constant with Fr and F_ri, improving primarily with larger _H̃i and _Sh.