The Evolution of Boundary Pressure in Ocean Basins

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Abstract
The boundary pressure adjustment process on an ocean basin scale is elucidated in two sets of numerical experiments. First, an initial-value problem is posed in a primitive equation shallow-water model that leads to significant changes in the pressure averaged along the boundary in a closed rectangular ocean basin. These results are compared with the analogous problem in a shallow-water quasigeostrophic model where the boundary pressure adjustment is parameterized by a consistency constraint that closes the mass, circulation, and energy balances in quasigeostrophy. There is very good agreement in the evolution of the boundary-average pressure and qualitative agreement in the evolution of the balanced motions in the interior. Second, idealized Kelvin wave experiments are posed in the primitive equation system on an f plane, a β plane, and a β plane in a domain of doubled dimensions. For β≠0, a scattering process is evident as the initial Kelvin wave transits the first meridional boundary it encounters. Two distinct scattering products are observed. In one there is a mass flux out of the coastal waveguide into the balanced interior motions that occurs on a time scale comparable to the basin circuit lime for the initial Kelvin wave. The second scattering product occurs in the wake of the Kelvin wave within the waveguide, forming a basin-scale coastal current. The relevant time scale for the waveguide scattering product is comparable to the time required to equilibrate the mass anomaly imposed in the waveguide by the Kelvin wave initial condition. The experiments demonstrate a coupling between short time scale motions of the coastal waveguide and longer time scale motions on the ocean interior. Implications of these processes are assessed for both these model problems and more general problems of transient ocean dynamics.

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