A study of wave attenuation over a Maxwell model of a muddy bottom

An extension to the wave attenuation over a muddy seabed is presented, in which Maxwell model is adopted as a candidate for fluidized seabed. For a very thin layer of Maxwell fluid, we present a new set of Boussinesq-type equations, in which the leading order influence of the Maxwell fluid layer appears in the source term of the continuity equation. Applying these equations to one-dimensional case, we obtain the damping rate of linear long waves and the evolution formula of solitary wave amplitude. Degenerating to Newtonian case, our results are consistent with those of Liu and Chan [1]. For the large relaxation time λ, we find that the damping rate of linear long waves is dominated by low-order modals and reaches peaks near the resonance points, and shear wave induced by solitary waves propagates along the vertical direction in the mud layer, which prolongs the damping process and leads to a second trough in the time history of bottom shear stress.