Axisymmetric viscous gravity currents flowing over a porous medium

TL;DR

This paper models the axisymmetric flow of viscous gravity currents over porous media, analyzing steady states and drainage, with experiments showing the influence of medium structure on flow behavior.

Contribution

It introduces a numerical and analytical model for viscous gravity currents over porous media, highlighting the effects of medium geometry and permeability on flow dynamics.

Findings

Good agreement between experiments and theory for tube media.

Unexpected overshoot and retreat observed with bead media.

Porous medium structure significantly affects flow behavior.

Abstract

We study the axisymmetric propagation of a viscous gravity current over a deep porous medium into which it also drains. A model for the propagation and drainage of the current is developed and solved numerically in the case of constant input from a point source. In this case, a steady state is possible in which drainage balances the input, and we present analytical expressions for the resulting steady profile and radial extent. We demonstrate good agreement between our experiments, which use a bed of vertically aligned tubes as the porous medium, and the theoretically predicted evolution and steady state. However, analogous experiments using glass beads as the porous medium exhibit a variety of unexpected behaviours, including overshoot of the steady-state radius and subsequent retreat, thus highlighting the importance of the porous medium geometry and permeability structure in these systems.