Stratified turbulence at the buoyancy scale

Numerical simulations of forced stratified turbulence are presented, and the dependence on horizontal resolution and grid aspect ratio is investigated. Simulations are designed to model the small-scale end of the atmospheric mesoscale and oceanic submesoscale, for which high horizontal resolution is usually not feasible in large-scale geophysical fluid simulations. Coarse horizontal resolution, which necessitates the use of thin grid aspect ratio, yields a downscale stratified turbulence energy cascade in agreement with previous results. We show that with increasing horizontal resolution, a transition emerges at the buoyancy scale 2πU/N, where U is the rms velocity and N is the Brunt–Väisälä frequency. Simulations with high horizontal resolution and isotropic grid spacing exhibit a spectral break at this scale, below which there is a net injection of kinetic energy by nonlinear interactions with the large-scale flow. We argue that these results are consistent with a direct transfer of energy to the buoyancy scale by Kelvin–Helmholtz instability of the large-scale vortices. These findings suggest the existence of a distinct subrange of stratified turbulence between the buoyancy and Ozmidov scales. This range must be at least partially resolved or parameterized to obtain robust simulations of larger-scale turbulence.