Physical and Computational Issues in the Numerical Modeling of Ocean Circulation

The large-scale circulation of the world’s oceans can be modeled by systems of partial differential equations of fluid dynamics, as scaled and parameterized for oceanic flows. This paper outlines some physical, mathematical, and computational aspects of such modeling. The topics include multiple length, time, and mixing scales; the choice of vertical coordinate; properties of the shallow water equations for a singlelayer fluid, including effects of the rotating reference frame; a statement of the governing equations for a three-dimensional stratified fluid with an arbitrary vertical coordinate; time-stepping and multiple time scales; and various options for spatial discretizations.