Frontal Geostrophic Dynamics

Abstract

From the primitive equations simplified dynamics are derived that apply to frontal situations in which interface slopes are important. The formalism, which eliminates inertial motions, is not Unlike the derivation of the quasi-geostrophic equation. The difference is two-fold: while quasi-geostrophic dynamics apply for length scales on the order of the deformation radius with limitation to small interface variations, frontal geostrophic dynamics apply for finite interface variations but only at length scales large compared to the deformation radius (three or more times). When the length scale is on the order of the deformation radius and, simultaneously, the interface variations are finite, inertial oscillations cannot be filtered out, and the primitive equations ought to be retained. In a reduced-gravity context, frontal geostrophic dynamics yield a single equation for the upper-layer depth. Although this equation is cubic in the depth variable, it is nonetheless considerably simpler than the primitive equations. It is suggested that the use of this equation can further advance the theoretical investigation of frontal dynamical processes. Some particular solutions are presented as illustrations. A new breed of waves is discovered. These waves propagate downstream (with the front on their left in the Northern Hemisphere) and are dispersive. They are unlike either Kelvin, Rossby or edge waves. Finally, a solution that corresponds to a time-dependent elliptical warm-core ring is also presented.