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Ocean barotropic vorticity balances: theory and application to numerical models
  • Robin Waldman,
  • Hervé Giordani
Robin Waldman
Centre National de Recherches Météorologiques (CNRM), Météo France/CNRS

Corresponding Author:[email protected]

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Hervé Giordani
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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.