High frequencies in random forcing affect turbulence simulations

Idealized simulations of atmospheric and oceanic turbulence often use random forcing to create large-scale vortices. Forcing is usually random in time, with white noise forcing being the most common approach. Vortices in nature, however, tend to evolve more slowly compared to the high frequencies found in white noise.

Applied mathematician Michael Waite wanted to look deeper at how high frequencies in random forcing affect simulated turbulence and whether they enhance the generation of waves from vortices. In Physics of Fluids, he reports on numerical simulations of rotating stratified turbulence with random forcing of large-scale geostrophic modes.

The simulations, designed as an idealization of atmospheric mesoscale turbulence, employed red noise forcing over a range of decorrelation time scales. Short time scales — as in, almost white noise — led to 46 percent more inertia-gravity wave energy than longer time scales, which were similar to or longer than the vortex time scale.

Waite suspects that this effect is due to wave-vortex interactions. Waves feel the high frequencies in the forcing through nonlinear interactions with the vortices, and when the forcing has significant energy at frequencies around the linear wave frequency, energy transfer is enhanced. Overall, Waite recommends that white noise forcing should be avoided for future simulations even if only applied to geostrophic motion.

Although he wasn’t surprised by these findings, Waite describes the problem as satisfying to investigate since it hadn’t been previously studied. Next, he wants to investigate what the correct time scale of forcing should be for more accurate simulations of atmospheric and oceanic turbulence.

Source: “Random forcing of geostrophic motion in rotating stratified turbulence,” by Michael L. Waite, Physics of Fluids (2017). The article can be accessed at https://doi.org/10.1063/1.5004986 .