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, $\beta$ . 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, $\widehat {T}^{{W}}$ , has a strong dependence on both bottom drag strength and planetary $\beta$ . At the deformation scale $\widehat {T}^{{W}}$ is always negative, representing the conversion of EAPE to EKE via baroclinic instability. For strong, linear bottom drag, $\widehat {T}^{{W}}$ 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 $\beta$ , $\widehat {T}^{{W}}$ 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 $\beta$ , 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 $\widehat {T}^{{W}}$ , occur at the meridional wavenumber corresponding to the jet spacing, with no zonal wavenumber component, i.e., $k_{x}=0$ . Importantly, the traditional source of large-scale EAPE, barotropic stirring of the baroclinic mode, is not a part of this $k_{x} = 0$ 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.