An LES Model for Wind Farm-Induced Atmospheric Gravity Wave Effects Inside Conventionally Neutral Boundary Layers

Abstract. The interaction of large wind farm clusters with the thermally-stratified atmosphere has emerged as an important physical process that impacts the productivity of wind farms. Under stable conditions, this interaction triggers the creation of atmospheric gravity waves (AGWs) due to the vertical displacement of the boundary layer by the wind farm. AGWs induce horizontal pressure gradients within the boundary layer that alter the wind speed distribution within the farm, influencing both wind farm power generation and wake development. Additional factors, such as the growth of an internal boundary layer originating from the wind farm entrance and increased turbulence due to the wind turbines, further contribute to wake evolution. Recent studies have highlighted the considerable computational cost associated with simulating gravity wave effects within large eddy simulations (LES), as a significant portion of the free atmosphere must be resolved due to the large vertical spatial scales involved. Additionally, specialized boundary conditions are required to prevent wave reflections from contaminating the solution. In this study, we introduce a novel methodology to model the effects of AGWs without extending the LES computational domain into the free atmosphere. The proposed approach addresses the wave reflection problem inherently, eliminating the need for these specialized boundary conditions. We utilize the recently developed multi-scale coupled (MSC) model of Stipa et al. (2023b) to estimate  the vertical boundary layer displacement triggered by the wind farm, and apply the deformation to the domain of an LES that extends only to the inversion layer. We validate our AGW modeling technique for two distinct free atmosphere stability conditions, comparing it to the traditional approach in which AGWs are fully resolved using a domain extending several kilometers into the free atmosphere. The proposed approach accurately captures AGW effects on the row-averaged thrust and power distribution of wind farms while demanding less than 15 % of the computational resources compared to traditional methods. This can be further reduced in cases of conventionally neutral boundary layers, since there is no longer a need for solving the potential temperature equation. The developed approach is used to compare global blockage and pressure disturbances obtained from the simulated cases against a solution characterized by zero boundary layer displacement, which represents a limiting case of very strong free atmosphere stratification. Finally, we discuss the implications of making such "rigid-lid" approximation, instead of considering the full gravity wave solution, when predicting wind farm power.