A Model of Incompressible-Fluid Flow with a Free Surface in a Highly Porous Medium

Abstract

A model is proposed for modeling a slow (inertialess) flow of a thin layer of viscous incompressible fluidwith a free surface inside a highly porousmediumabove an impermeable surface. The fluid flow is described by the Brinkman filtration law, on the bottom boundary the Navier slip condition is prescribed. The equation for the fluid layer thickness is obtained, which has the form of a special case of a nonlinear heat conduction equation. Solutions in the form of traveling waves and self-similar solutions describing the fluid spreading are investigated.