Nonlinear energy transfers and phase diagrams for geostrophically balanced rotating--stratified flows

Equilibrium statistical mechanics tools have been developed to obtain indications about the natural tendencies of nonlinear energy transfers in two-dimensional and quasi two-dimensional flows like rotating and stratified flows in geostrophic balance. In this article, we consider a simple model of such flows with a non-trivial vertical structure, namely two-layer quasi-geostrophic flows, which remain amenable to analytical study. We obtain the statistical equilibria of the system in the case of a linear vorticity-stream function relation, build the corresponding phase diagram, and discuss the most probable outcome of nonlinear energy transfers, both on the horizontal and on the vertical, in the presence of stratification and rotation.