A Nonhydrostatic Mesoscale Ocean Model. Part I: Well-Posedness and Scaling

The incompressibility and hydrostatic approximations that are traditionally used in large-scale oceanography to make the hydrodynamic equations more amenable to numerical integration result in the primitive equations. These are ill-posed in domains with open boundaries and hence not well-suited to mesoscale or regional modeling. Instead of using the hydrostatic approximation, the authors permit a greater deviation from hydrostatic balance than what exists in the ocean to obtain a system of equations that is well-posed with the specification of pointwise boundary conditions at open or solid boundaries. These equations, formulated with a free-surface boundary, model the mesoscale flow field accurately in all three-dimensions, even the vertical. It is essential to retain the vertical component of the Coriolis acceleration in the model since it is nonhydrostatic.