A four-dimensional primitive equation model for coupled coastal - deep ocean studies

Abstract

A prototype four-dimensional (x,y,z,t) continental shelf/deep ocean model is described. In its present form, the model incorporates the effects of finite-amplitude topography, advective nonlinearities, and variable stratification and rotation. The model can be forced either directly by imposed atmospheric windstress and surface pressure distributions, and energetic mean currents imposed by the exterior oceanic circulation; or indirectly by initial distributions of shoreward propagating mesoscale waves and eddies. To avoid concerns over the appropriate specification of "open" boundary conditions on the cross-shelf and seaward model boundaries, a periodic channel geometry (oriented along-coast) is used. The model employs a traditional finite-difference expansion in the cross-shelf direction, and a Fourier (periodic) representation in the long-shelf coordinate. A modified sigma coordinate system, and a Chebyshev-tau approximation scheme, are used to incorporate the vertical dependence. The model has been validated against a variety of propagating topographic wave problems. Representative run times and error estimates are given.