Viscous Damping of Cnoidal Waves Over Fluid‐Mud Seabed

The heights of water waves propagating over fluid‐mud bottom can be significantly reduced due to the viscous energy dissipation occurring in the mud bottom. In some cases, exceptionally high rates of attenuation are possible whereby waves are almost completely damped within several wavelengths. This phenomenon has been observed both in field investigation and in laboratory experimentation. In this paper, the viscous damping of cnoidal waves progressing over fluid‐mud seabeds is investigated, in which fluid mud is assumed to be a viscous fluid. The theoretical model adopted here is a two‐layer viscous fluid model modified with three boundary layers at the water‐mud interface and at the rigid bottom beneath mud layer. Viscosities of both water and fluid mud are taken into consideration. For a nonlinear shallow wave progressing over a viscous mud bed, the first‐order analytical solutions are derived for the velocity distributions in boundary layers and for the attenuation rate of wave heights with distance. The attenuation coefficients are larger than those predicted on the basis of linear shallow wave theory, and unlike the case of linear shallow waves, they are not independent of wave height. The viscous damping of solitary and sinusoidal waves, which are two extreme cases of cnoidal wave, are also discussed according to the present solution.