The attenuation of water waves over a non-rigid bed

Water waves that propagate over a non-rigid bed are attenuated as a result of energy dissipation within the bed. This paper describes the analysis, from the basis of small-amplitude wave theory, of the coupled interaction between the bed, which responds in both an elastic and viscous manner, and an overlying layer of inviscid fluid. A dispersion relation is derived, from which rates of wave attenuation and sea bed deflexions are calculated. The results are relevant wherever the sea bed, in its response to water waves, is non-rigid, as is often the case in coastal waters. Depending on the elasticity and viscosity of the sea bed, the wave attenuation can be of the same or of a larger order of magnitude than that due to bottom friction or percolation in a permeable bed. Where waves propagate over a soft viscous bed, for example as is the case at certain mud flats off the south-west coast of India, exceptionally high rates of attenuation are possible whereby waves are almost completely damped within several wavelengths.