On the damping of gravity waves propagated over a permeable surface

Abstract

The problem of the damping of small amplitude gravity waves propagated over a permeable sea bed is examined in terms of viscous-flow theory. Previous solutions for the exponential loss of wave height with distance consider either viscous damping over an impermeable bed, for example, Biesel [1949], or inviscid potential flow over a permeable bed, Reid and Kajiura [1957]. A solution is obtained which satisfies the full viscous boundary conditions, and for small values of the viscosity and permeability the damping is found to be the sum of these two solutions. This result agrees reasonably well with measurements by Savage [1953] on waves over a smooth sand bed. It is also found that to a first approximation viscosity slightly lengthens the classical free-wave period in shallow water, while permeability does not.