A unified asymptotic derivation of two-layer, frontal geostrophic models including planetary sphericity and variable topography

Abstract

A general asymptotic theory for two-layer, frontal geostrophic (FG) models including the effects of planetary sphericity and variable bottom topography is developed. In addition to the standard β-plane approximation, an additional baroclinic correction associated with planetary sphericity, the Veronis effect, enters into the leading-order dynamics of FG models. The Veronis effect depends on the variation of the longitudinal metric as the transformation to Cartesian coordinates is made. The Veronis effect becomes significant at mid to high latitudes for the long length scales associated with FG models which are larger than the internal Rossby radius of deformation. The inclusion of variable bottom topography results in an asymmetry between the dynamics of surface and bottom-trapped currents. Variable bottom topography enters the equations in a similar, but not identical, manner to the β effect. The asymmetry between the dynamics of surface-intensified and bottom-intensified FG currents over sloping topography occurs due to the fact that topography stabilizes surface flows while it destabilizes bottom flows. Physically, the asymmetry arises because sloping topography provides a stabilizing background vorticity gradient for surface-intensified flows. However, for the bottom-intensified flow of a relatively dense water mass, the presence of a sloping bottom allows the continual release of gravitational potential energy as the center of mass of the dense water “slides” down the sloping bottom and is thus a destabilizing rather than a stabilizing effect.