A coupled model of interior balanced and boundary flow
Résumé
Ocean circulation modeling requires parameterizations of sub-grid scale processes, which in turn involves two separate issues. First, the parameterization should mirror the effect of important sub-grid dynamics and second, constants and boundary conditions as required by the parameterization must be determined. In modern ocean circulation modeling, many parameterizations take the form of viscous operators with poorly known coefficients, and the boundary conditions options are free-slip, partial-slip or no-slip, suitably adjusted for the order of the operator. The extent to which viscous operators are dynamically apt is unclear and there is virtually no dynamical guidance on how to choose between the boundary conditions. Often the decision about the suitability of the parameterizations and the boundary conditions is made based on qualitative characteristics of the solution, which is somewhat subjective. Here, a dynamical boundary layer model is developed that explicitly determines the boundary potential vorticity fluxes resulting from the sub-grid scale interactions of the resolved flow with the boundaries. When applied to a quasi-geostrophic model, comparisons of model evolution with high resolution primitive equation simulations are favorable. The recipe outlined here, while far from a complete parameterization of boundary dynamics, represents a step toward resolving the issues currently surrounding sub-grid scale parameterization. The results also argue that boundary dynamics naturally dissipate balanced energy and are likely to represent a principal means by which the oceanic mesoscale energy budget is balanced.