Simple models of Coriolis-influenced axisymmetric particle-driven gravity currents

Approximate analytical results are obtained for the propagation of an axisy mmetric gravity current in a system rotating around a vertical axis, which occurs when a dense fluid intrudes horizontally under a lighter ambient flu id. Situations for which the density difference between the fluid is due ei ther to compositional differences or to suspended particulate matter are co nsidered; for the the latter, particle-driven cases, two models for the par ticle transport, turbulent remixing and laminar sedimentation are implement ed. Attention is focused on situations in which the apparent importance of the Coriolis terms relative to the inertial terms, represented by the param eter C (the inverse of a Rossby number), is not large. A box-model approxim ation is used, in which the current is described as a control volume compos ed of a cylinder with a conical "roof' subject to global conservation condi tions and simplifying assumptions. This leads to ordinary differential equa tions from which it is possible to calculate readily such essential feature s as the behaviour of the radius of propagation, height of the head (nose) and the amount of settled particles (when applicable). In particular, the l imitation imposed by the Coriolis effects on the radius of propagation, the time of attainment of the maximal spread, and the appearance of an attache d reverse motion are properly reflected. For the particle-driven case a par ametric dependency between the settling and Coriolis influences is obtained , which allows for a stringent comparison to be made between the two differ ent particle-transport models. The box model results are in good qualitativ e agreement with numerical solutions of the full shallow-water equations, f or which a novel similarity transform is also presented. (C) 1999 Elsevier Science Ltd. All rights reserved.