Generation of turbulence through frontogenesis in sheared stratified flows

Abstract

The large-scale structures in the ocean and the atmosphere are in geostrophic balance, and a conduit must be found to channel the energy to the small scales where it can be dissipated. In turbulence, this takes the form of an energy cascade, whereas a possible mechanism in a balanced flow is through the formation of fronts, a common occurrence in geophysics. We show that an iconic configuration in laboratory and numerical experiments for the study of turbulence, the so-called Taylor-Green or von Kármán swirling flow, can be suitably adapted to domains with large aspect ratios, leading to the creation of an imposed large-scale vertical shear. To this effect, we use direct numerical simulations of the Boussinesq equations without net rotation and with no small-scale modeling. Various grid spacings are used, up to 20482 × 256 spatial points. The grids are always isotropic, with box aspect ratios of either 1:4 or 1:8. We find that when shear and stratification are comparable, the imposed shear layer resulting from the forcing leads to the formation of fronts and filaments which destabilize and evolve into a turbulent flow in the bulk, with a sizable amount of dissipation and mixing, following a cycle of front creation, instability, and development of turbulence. The results depend on the vertical length scales of shear and stratification.