We examine the motion of a two-layer gravity current, composed of two fluids of
different viscosity and density, as it propagates through a model porous layer. We
focus on two specific situations: first, the case in which each layer of fluid has finite
volume, and secondly, the case in which each layer is supplied by a steady maintained
flux. In both cases, we find similarity solutions which describe the evolution of the
flow. These solutions illustrate how the morphology of the interface between the
two layers of fluid depends on the viscosity, density and volume ratios of the two
layers. We show that in the special case that the viscosity ratio of the upper to
lower layers, V, satisfies V = (1 + F)/(1 + RF)
where F and R are respectively the
ratios of the volume and buoyancy of the lower layer to those of the upper layer,
then the ratio of layer depths is the same at all points. Furthermore, we show
that for V > (<)(1 + F)/(1 + RF), the lower (upper) layer advances ahead of the
upper (lower) layer. We also present some new laboratory experiments on two-layer
gravity currents, using a Hele-Shaw cell, and show that these are in accord with the
model predictions. One interesting prediction of the model, which is confirmed by
the experiments, is that for a finite volume release, if the viscosity ratio is sufficiently
large, then the less-viscous layer separates from the source. We extend the model to
describe the propagation of a layer of fluid which is continuously stratified in either
density or viscosity, and we briefly discuss application of the results for modelling
various two-layer gravity-driven flows in permeable rock.