On gravity currents propagating at the base of a stratified ambient: effects of geometrical constraints and rotation
MARIUS UNGARISH a1andHERBERT E. HUPPERT a2 a1 Department of Computer Science, Technion, Haifa 32000, Israel a2 Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
The behaviour of an inviscid gravity current released from a lock and propagating over a horizontal boundary at the base of a stratified ambient fluid is considered in the framework of a one-layer shallow-water formulation. Solutions for two-dimensional rectangular and axisymmetric geometries, with emphasis on the rotation of the latter, were obtained by a Lax–Wendroff scheme. Box-model approximations are also discussed. The axisymmetric and rotating case admits steady-state lens structures, for which approximate and numerical solutions are presented. In general, the stratification reduces the velocity of propagation and enhances the Coriolis effects in a rotating system (in particular, the maximal radius of propagation decreases). Comparisons of the shallow-water results with Navier–Stokes simulations and laboratory experiments indicate good agreement, at least for the initial period of propagation. The major deficiency of this shallow-water model is the lack of incorporation of internal waves. In particular, if the propagation is at subcritical speed, the applicability of the model is restricted to the time prior to the first effective interaction between the head of the gravity current and the lowest-order internal wave; an estimate of this position is presented.