Abstract
Mass conservation is used to elucidate differences between initial boundary value problems for the quasi-geostrophic vorticity equation in regions that are fully enclosed versus regions that are partially open. In fully closed domains, mass conservation is explicitly imposed as a consistency constraint on the dynamical evolution of the flow. Partially or fully open domains do not require an explicit mass conservation constraint. In these cases, the mass conservation balance is used as a diagnostic to describe the interaction between open boundary conditions and the inflow/outflow vorticity implied by the quasi-geostrophic equation. The new formalism is carried over the multiply connected, partially open domains, where explicit circulation integral constraints are required around island boundaries. Implications concerning coastal applications of quasi-geostrophic numerical models are outlined.
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