Analytical solutions in a hydraulic model of seepage with sharp interfaces

Flows in horizontal homogeneous porous layers are studied in terms of a hydraulic model with an abrupt interface between two incompressible Darcian fluids of contrasting density driven by an imposed gradient along the layer. The flow of one fluid moving above a resting finger-type pool of another is studied. A straight interface between two moving fluids is shown to slump, rotate and propagate deeper under periodic drive conditions than in a constant-rate regime. Superpropagation of the interface is related to Philip's superelevation in tidal dynamics and acceleration of the front in vertical infiltration in terms of the Green-Ampt model with an oscillating ponding water level. All solutions studied are based on reduction of the governing PDE to nonlinear ODEs and further analytical and numerical integration by computer algebra routines.