Theoretical Model for Nonlinear Long Waves over a Thin Viscoelastic Muddy Seabed

Abstract

We theoretically analyzed the interaction between surface water waves and a thin muddy seabed. Wave motion in the inviscid water layer was assumed to be irrotational and the soft mud was modeled as a linear viscoelastic fluid. Under the Boussinesq approximation for nonlinear long waves, we present a set of depth-integrated equations that can be solved for the depth-averaged horizontal water particle velocity and the free-surface displacement. The long wave model needs to be solved numerically in general. For the cases of linear progressive waves and solitary waves, further analytical solutions were obtained. The model-predicted wave amplitude attenuation rate was shown to reasonably agree with the field data. Our analysis suggests that the elasticity of mud can potentially enhance the wave damping efficiency of a muddy seabed. The present formulations generalize several existing linear and nonlinear models for the wave–mud problem reported in literature.