Investigating the Relationship between Simulation Parameters and Flow Variables in Simulating Atmospheric Gravity Waves in Wind Energy Applications

Abstract: Wind farms, particularly offshore clusters, are becoming larger than ever before. Besides influencing wind farms and local meteorology downstream, large wind farms can trigger atmospheric gravity waves in the inversion layer and the free atmosphere aloft. Wind farm-induced gravity waves can cause adverse pressure gradients upstream of the wind farm, that contribute to the global blockage effect, and favorable pressure gradients above and downstream of the wind farm that enhance wake recovery. Numerical modeling is a powerful means of studying wind farm-induced atmospheric gravity waves, but it comes with the challenge of handling spurious reflections of these waves from domain boundaries. Approaches like radiation boundary conditions and forcing zones are used to avoid the reflections. However, the simulation setup heavily relies on ad-hoc processes. For instance, the widely used Rayleigh damping method requires ad-hoc tuning to acquire a setup only applicable to a particular case. To surmount this hurdle, we conduct a systematic LES study for flow over a 2D hill and through wind farm canopies that explores the dependence of domain size and damping layer setup on parameters driving linearly stratified atmospheric flows. Mainly the internal waves in the free atmosphere reflect from the boundaries, therefore by simulation linearly stratified conditions we focus on internal waves only. The Froude number drives most of the internal wave properties, such as wavelengths, amplitude, and direction. Therefore, the domain sizing and Rayleigh damping layer setup mainly depends on the Froude number. We anticipated the effective wavelengths to be the correct length scale to size the domain and damping layer thickness. Also, the damping coefficient is scaled with Brunt-V\"ais\"al\"a frequency.