A horizontally homogeneous two-layer quasigeostrophic model with imposed environmental vertical shear is used to study eddy energies and fluxes in the regime in which an inverse barotropic energy cascade excites eddies of much larger scale than the deformation radius. It is shown that the eddy potential vorticity flux, “thickness” flux, and the extraction of energy from the background flow are dominated by the largest eddies excited by the cascade, and not by deformation-scale eddies. The role of the latter is a catalytic one of transferring the baroclinic energy cascading downscale into the barotropic mode, thereby energizing the inverse cascade.
Based on this picture, scaling arguments are developed for the eddy energy level and potential vorticity flux in statistical equilibrium. The potential vorticity flux can be thought of as generated by a diffusivity of magnitude Ukd/k20, where U is the difference between the mean currents in the two layers, kd is the inverse of the deformation radius, and k0 is the wavenumber of the energy-containing eddies. This result is closely related to that proposed by Green, although the underlying dynamical picture is different.