Covariant equations for geophysical fluids with an asymmetric gravitational potential and their hydrostatic limit

Abstract

Starting from the governing equations in tensor form for non-hydrostatic fluid dynamics, the hydrostatic limit is obtained by introducing a scaling parameter. This allows the use of the same fundamental tensor equations to describe the dynamics of non-hydrostatic and hydrostatic geophysical fluids, possibly combined with geometric approximations, while preserving the dynamical consistency of the governing equations in arbitrary coordinates. This provides the tools to reproduce in a systematic manner the quartet of equations-deep/non-hydrostatic, deep/hydrostatic, shallow/non-hydrostatic, and shallow/hydrostatic-presented elsewhere. This quartet is generalised to the case where the gravitational potential has no spatial symmetries.