  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.
