Free-surface flow in porous media and periodic solution of the shallow-flow approximation

The equations describing the flow of liquid in a porous medium with a free surface are expanded when the shallow-flow assumption holds. Second-order theory is used to describe the propagation of steady periodic motion in the medium, driven by the oscillating level of a reservoir in contact with it. A linearized solution of the second-order theory is compared with a numerical solution and is found adequate even when the amplitude of the motion is comparable to the mean depth of the liquid. The predictions of the analysis are found in good agreement with two laboratory experiments.