Propagation of Nonlinear Surface Waves over Viscoelastic Mud

Mud is ubiquitous in coastal waters, and it is well known that surface waves dissipate strongly over a muddy seabed. An accurate model for wave evolution requires an accurate characterization of mud rheology. There has been several assumptions for mud rheology. In this study, we incorporate a mud-induced damping mechanism in a frequency-domain phase-resolving nonlinear wave model. The mud layer is assumed to be thin and behave as a viscoelastic medium. First, model results for monochromatic surface waves are compared with laboratory experiments and a good comparison is obtained. It is shown that increasing the mud elasticity results in a decrease in damping and an increase in phase-shift from the case with a purely viscous mud. The validated model is then employed to examine the combined effect of mud viscosity and elasticity on evolution of surface wave spectrum. Two-dimensional simulations demonstrate strong wave dissipation over a mud patch resulting in a significant diffraction in the lee side.