Baroclinic energy cycles in two-layer quasi-geostrophic turbulence

We consider the two-layer quasi-geostrophic model with linear bottom friction and, in certain simulations, a planetary vorticity gradient, β . We derive energy budgets in wavenumber space for eddy available potential energy (EAPE), baroclinic eddy kinetic energy (EKE) and barotropic EKE, a particular decomposition that has previously been overlooked. The conversion between EAPE and baroclinic EKE, T^W , has a strong dependence on both bottom drag strength and planetary β . At the deformation scale T^W is always negative, representing the conversion of EAPE to EKE via baroclinic instability. For strong, linear bottom drag, T^W is positive at large scales due to frictional energisation of the baroclinic mode, providing a large-scale EAPE source. With weak-to-moderate bottom drag and moderate-to-strong planetary β , T^W is the dominant source of EAPE at large scales, converting baroclinic EKE that has experienced a baroclinic inverse cascade back into EAPE, and thus closing a novel and exclusively baroclinic energy loop. With planetary β , zonal jets form and the dominant large-scale processes in the energy cycle of the system, e.g. barotropic dissipation and the peak of positive T^W , occur at the meridional wavenumber corresponding to the jet spacing, with no zonal wavenumber component, i.e., kₓ=0 . Importantly, the traditional source of large-scale EAPE, barotropic stirring of the baroclinic mode, is not a part of this kₓ = 0 energy cycle, and thus plays a secondary role. The results suggest that consideration of horizontally two-dimensional processes is requisite to understand the energetics and physics of baroclinic geophysical jets.