The equations for mass, momentum, temperature and salinity are formulated in a non-inertial general curvilinear coordinate system to be solved numerically. A flux-difference split type of numerical flux formulation is used for the convective fluxes and the equations are numerically solved in a strongly coupled manner using the discretized Newton-relaxation scheme. The addition of artificial viscosity is not required for stability. Test cases were considered that included laminar flow over a flat plate with prescribed wall temperature and salinity as well as laminar flow with heat transfer over a backward facing step. These computations compare well with existing results. The present numerical scheme was also applied to a body-fitted grid that approximates the entire Atlantic Ocean and rotates with the Earth. These results, though encouraging, must be considered preliminary.>