The climatological mean barotropic vorticity budget is analyzed to investigate the relative importance of surface wind stress, topography and nonlinear advection in dynamical balances in a global ocean simulation. In addition to a pronounced regional variability in vorticity balances, the relative magnitudes of vorticity budget terms strongly depend on the length-scale of interest. To carry out a length-scale dependent vorticity analysis in different ocean basins, vorticity budget terms are spatially filtered by employing the coarse-graining technique. At length-scales greater than 10o (or roughly 1000 km), the dynamics closely follow the Topographic-Sverdrup balance in which bottom pressure torque, surface wind stress curl and planetary vorticity advection terms are in balance. In contrast, when including all length-scales resolved by the model, bottom pressure torque and nonlinear advection terms dominate the vorticity budget (Topographic-Nonlinear balance), which suggests a prominent role of oceanic eddies, which are of Ο(10-100) km in size, and the associated bottom pressure anomalies in local vorticity balances at length-scales smaller than 1000 km. Overall, there is a transition from the Topographic-Nonlinear regime at scales smaller than 10o to the Topographic-Sverdrup regime at length-scales greater than 10o. These dynamical balances hold across all ocean basins; however, interpretations of the dominant vorticity balances depend on the level of spatial filtering or the effective model resolution. On the other hand, the contribution of bottom and lateral friction terms in the barotropic vorticity budget remains small and is significant only near sea-land boundaries, where bottom stress and horizontal friction generally peak.

The mixing of tracers by mesoscale eddies, parameterized in many ocean general circulation models (OGCMs) as a diffusive-advective process, contributes significantly to the distribution of tracers in the ocean. In the ocean interior, diffusive contribution occurs mostly along the direction parallel to local neutral density surfaces. However, near the surface of the ocean, small-scale turbulence and the presence of the boundary itself break this constraint and the mesoscale transport occurs mostly along a plane parallel to the ocean surface (horizontal). Although this process is easily represented in OGCMs with geopotential vertical coordinates, the representation is more challenging in OGCMs that use a general vertical coordinate, where surfaces can be tilted with respect to the horizontal. We propose a method for representing the diffusive horizontal mesoscale fluxes within the surface boundary layer of general vertical coordinate OGCMs. The method relies on regridding/remapping techniques to represent tracers in a geopotential grid. Horizontal fluxes are calculated on this grid and then remapped back to the native grid, where fluxes are applied. The algorithm is implemented in an ocean model and tested in idealized and realistic settings. Horizontal diffusion can account for up to 10\% of the total northward heat transport in the Southern Ocean and Western boundary current regions of the Northern Hemisphere. It also reduces the vertical stratification of the upper ocean, which results in an overall deepening of the surface boundary layer depth. Lastly, enabling horizontal diffusion leads to meaningful reductions in the near-surface global bias of potential temperature and salinity.

The mixing of tracers by mesoscale eddies, parameterized in many ocean general circulation models (OGCMs) as a diffusive process, contributes significantly to the distribution of tracers in the ocean. In the ocean interior, such processes occur mostly along the direction parallel to the local neutral density surface. However, near boundaries, small-scale turbulence breaks this constraint and the mesoscale transport occurs mostly along a plane parallel to the boundary (i.e., laterally near the surface of the ocean). Although this process is easily represented in OGCMs with geopotential vertical coordinates, the representation is more challenging in OGCMs that use a general vertical coordinate, where surfaces can be tilted with respect to the horizontal. We propose a method for representing the diffusive lateral mesoscale fluxes within the surface boundary layer of general vertical coordinate OGCMs. The method relies on regridding/remapping techniques to represent tracers in a geopotential grid. Lateral fluxes are calculated in this grid and then remapped back to the native grid, where fluxes are applied. The algorithm is implemented in an ocean model and tested in idealized and realistic settings. Lateral diffusion reduces the vertical stratification of the upper ocean, which results in an overall deepening of the surface boundary layer depth. Although the impact on certain global metrics is not significant, enabling lateral diffusion leads to a small but meaningful reduction in the near-surface global bias of potential temperature and salinity.