Ocean Barotropic Vorticity Balances: Theory and Application to Numerical Models

The barotropic vorticity (BV) balance is fundamental when interpreting the ocean gyre circulation. Here we propose an intercomparison of vorticity equations for the depth-integrated flow applied to ocean models. We review four distinct variants of the BV balances, each giving access to diagnostic equations for the depth-integrated 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 spatial 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 arise from interactions of the flow with slanting topography. We identify significant spurious topographic torques related to the model's C-grid discretizations, and we suggest ways to address them. In the depth-integrated and BV balances, bottom vortex stretching and bottom pressure torque drive the flow interaction with topography, respectively. Contrary to Sverdrup theory, the wind stress curl, although dominant in the interior Subtropics, becomes a minor player anywhere significant bottom velocities prevail. The geostrophic contour vorticity balance highlights the limits of barotropic models of the ocean circulation through the so-called JEBAR term. Finally, the transport divergence vorticity balance stresses the limitations of Ekman plus geostrophic dynamics for the mass balance closure in ocean models. This framework should encourage ocean modellers to diagnose more routinely momentum and vorticity equations.