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Equilibrium statistical mechanics tools have been developed to obtainindications about the natural tendencies of nonlinear energy transfers intwo-dimensional and quasi two-dimensional flows like rotating and stratifiedflows in geostrophic balance. In this article, we consider a simple model ofsuch flows with a non-trivial vertical structure, namely two-layerquasi-geostrophic flows, which remain amenable to analytical study. We obtainthe statistical equilibria of the system in the case of a linearvorticity-stream function relation, build the corresponding phase diagram, anddiscuss the most probable outcome of nonlinear energy transfers, both on thehorizontal and on the vertical, in the presence of stratification and rotation.

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