Damping of Gravity Waves Over Porous Bed

The damping of gravity waves over the contaminated free surface of a viscous layer of fluid that is bounded below by a porous bed is investigated. It is assumed that the bed is saturated with the same fluid. The coupled system of linearized equations appropriate to the fluid layer and the porous bed is solved to study the damping of a progressive wave on the surface of the fluid. The dispersion relation yielding the dependence of the frequency on the viscosity on the parameters related to the porous bed, and on the free surface film, is derived. The effect of the latter on the damping of the waves is found to be very significant. The results obtained subsume the hitherto known results of other authors.