The flow of an axisymmetric stratified gravity current into a stratified ambient in a rotating system

Abstract

The effect of rotation on the behaviour of an inviscid axisymmetric stratified gravity current released from a lock and propagating into a stratified ambient fluid is considered. It is assumed that both the ambient and the current are linearly stratified. We develop a one-layer shallow-water model and show that the flow is governed by four dimensionless parameters which represent the stratifications in the current and ambient, the ratio of Coriolis to inertia effects, and the height ratio of the ambient to the lock. The solution, obtained by a finite-difference method, provides the shape of the interface, radial and azimuthal speeds, and radius of propagation, as functions of time. The propagation reaches a maximum radius, dependent on the input parameters; the increase of the internal stratification reduces the radius. The system admits steady-state lens structures for which simple approximate solutions are also presented. In general, the internal stratification of the current reduces the velocity of propagation, and enhances the Coriolis effects in a rotating system.