The circulation of the ocean can be modeled by three-dimensional nonlinear systems of partial differential equations of fluid dynamics, as scaled and adapted for oceanic flows. The spatial discretization methods that are traditionally used to solve such systems have some deficiencies, and a promising alternative is to use discontinuous Galerkin (DG) methods. This talk will survey some of the advantages of this alternative and some of the issues that are encountered if DG methods are used in this situation. A particular point of attention will be the formulation of the pressure forcing. One issue is to express this forcing in a way that is natural for the weak form of the partial differential equation when using an arbitrary vertical coordinate. Another is the problem of accounting for lateral discontinuities in pressure without solving expensive three-dimensional Riemann problems.