GRAVITY-DRIVEN FLOWS IN POROUS LAYERS

The motion of instantaneous and maintained releases of buoyant fluid t hrough shallow permeable layers of large horizontal extent is describe d by a nonlinear advection-diffusion equation. This equation admits si milarity solutions which describe the release of one fluid into a hori zontal porous layer initially saturated with a second immiscible fluid of different density. Asymptotically, a finite volume of fluid spread s as t(1/3). On an inclined surface, in a layer of uniform permeabilit y, a finite volume of fluid propagates steadily alongslope under gravi ty, and spreads diffusively owing to the gravitational acceleration no rmal to the boundary, as on a horizontal boundary. However, if the per meability varies in this cross-slope direction, then, in the moving fr ame, the spreading of the current eventually becomes dominated by the variation in speed with depth, and the current length increases as t(1 /2). Shocks develop either at the leading or trailing edge of the flow s depending upon whether the permeability increases or decreases away from the sloping boundary. Finally we consider the transient and stead y exchange of fluids of different densities between reservoirs connect ed by a shallow long porous channel. Similarity solutions in a steadil y migrating frame describe the initial stages of the exchange process. In the final steady state, there is a continuum of possible solutions , which may include flow in either one or both layers of fluid. The ma ximal exchange flow between the reservoirs involves motion in one laye r only. We confirm some of our analysis with analogue laboratory exper iments using a Hele-Shaw cell.