Mesoscale eddies regulate the ocean heat and carbon budgets. However, how and where the kinetic energy flows out from the mesoscale reservoir remains uncertain. In this study, a simplified equation of the mesoscale energy budget is used to obtain a global estimation of the eddy dissipation rate. This framework is first validated in a global ocean model and then applied to a density climatology and a global reconstruction of the eddy kinetic energy field. We find a global disipation rate of 0.66±0.19 TW for the mesoscale kinetic energy, in agreement with recent independent estimates. The results also show an intense dissipation near western boundary currents and in the Antarctic Circumpolar Current, where both large levels of energy and baroclinic conversion occur. The resulting geographical distribution of the dissipation rate brings new insights for closing the ocean kinetic energy budget, as well as constraining future mesoscale parameterizations and associated mixing processes.

The barotropic vorticity balance is fundamental to interpret the ocean gyre circulation. However, it remains an overlooked diagnostic in ocean circulation models. Here we propose a general theory of barotropic vorticity balances for use in ocean models. We show that there exist four distinct barotropic vorticity balances, each giving access to diagnostic equations for the depth-integral ocean circulation, either meridional, across geostrophic contours or its divergence. We then formulate those balances in the Vorticity Balances in NEMO (VoBiN) diagnostic package aimed at the NEMO ocean platform and more generally C-grid ocean models. We show that space discretization of the equations of motion have profound implications for those vorticity balances. Finally, we diagnose the main balances of a global ocean climate simulation. In all vorticity balances, topographic torques, both physical and numerical, arise from interactions of the flow with slanting topography. Contrary to Sverdrup theory, the wind stress curl, although dominant in the interior Subtropics, becomes a minor player anywhere significant bottom velocities prevail. Depth-dependent vorticity dynamics show that the barotropic balance emerges from the coupling of the surface (frictional) and bottom (topographic) boundary layers to the geostrophic interior through the generation of vertical motion. The vorticity balance for the depth-averaged momentum equations highlights the limits of barotropic models of the ocean circulation. Finally, the vorticity balance for the transport divergence highlights the key role played by numerical torques for the oceanic mass balance. This framework should encourage ocean modellers to diagnose more routinely momentum and vorticity equations.