Waves over Soft Muds: A Two-Layer Fluid Model

The problem of water waves propagating over a mud bottom, characterized as a laminar viscous fluid, is treated in several ways. First, two complete models are present, each valid for different lower (mud) layer depths, and second, a boundary layer model is presented as an appendix for the case where the lower layer is thick with respect to the boundary layer. These models are compared to the shallow water model and experimental results of Gade (1957, 1958) and agree well. The results show that extremely high wave attenuation rates are possible when the thickness of the lower layer is the same order as the internal boundary layer thickness and when the lower layer is thick.