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

A general asymptotic theory for two-layer, frontal geostrophic (FG) models including the effects of planetary sphericity and variable bottom topograph y is developed. In addition to the standard beta-plane approximation, an ad ditional baroclinic correction associated with planetary sphericity, the Ve ronis effect, enters into the leading-order dynamics of FG models. The Vero nis effect depends on the variation of the longitudinal metric as the trans formation to Cartesian coordinates is made. The Veronis effect becomes sign ificant 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 betwee n the dynamics of surface and bottom-trapped currents. Variable bottom topo graphy enters the equations in a similar, but not identical, manner to the beta effect. The asymmetry between the dynamics of surface-intensified and bottom-intensified FG currents over sloping topography occurs due to the fa ct that topography stabilizes surface flows while it destabilizes bottom fl ows. Physically, the asymmetry arises because sloping topography provides a stabilizing background vorticity gradient for surface-intensified flows. H owever, for the bottom-intensified flow of a relatively dense water mass, t he presence of a sloping bottom allows the continual release of gravitation al 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 ef fect. (C) 1999 American Institute of Physics. [S1070-6631(99)03109-8].