Abstract

The damping of small-amplitude surface waves on a viscous fluid over a permeable fixed bed is studied. Conservation arguments and consideration of the rate of doing work at the fluid-bed interface are applied in a careful analysis of the boundary conditions at the interface. It is shown that stresses are not continuous at the interface. A general dispersion relationship, which gives the damping characteristics for given wave parameters, is found together with the stream functions for the flow in the two regimes. The wave damping characteristics are different from those given in previous studies of waves over a permeable fixed bed and are a consequence of the new boundary conditions derived below. The damping effects due to percolation in the fixed bed are not always small in comparison with the viscous effects. Some numerical examples of typical situations are given.

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