Balanced and unbalanced routes to dissipation in an equilibrated Eady flow

Abstract

The oceanic general circulation is forced at large scales and is unstable to mesoscale eddies. Large-scale currents and eddy flows are approximately in geostrophic balance. Geostrophic dynamics is characterized by an inverse energy cascade except for dissipation near the boundaries. In this paper, we confront the dilemma of how the general circulation may achieve dynamical equilibrium in the presence of continuous large-scale forcing and the absence of boundary dissipation. We do this with a forced horizontal flow with spatially uniform rotation, vertical stratification and vertical shear in a horizontally periodic domain, i.e. a version of Eady's flow carried to turbulent equilibrium. A direct route to interior dissipation is presented that is essentially non-geostrophic in its dynamics, with significant submesoscale frontogenesis, frontal instability and breakdown, and forward kinetic energy cascade to dissipation. To support this conclusion, a series of simulations is made with both quasigeostrophic and Boussinesq models. The quasigeostrophic model is shown as increasingly inefficient in achieving equilibration through viscous dissipation at increasingly higher numerical resolution (hence Reynolds number), whereas the non-geostrophic Boussinesq model equilibrates with only weak dependence on resolution and Rossby number.