The propagation of a solitary wave over seabed mud of the Voigt model

In shallow water, seabed mud can dissipate the energy of surface gravity waves effectively. In this paper, solitary wave attenuation induced by seabed mud is studied based on a two-layered system, in which the water is assumed to be inviscid and the mud layer is described by the Voigt model. A set of Boussinesq-type equations suitable for solitary waves over the mud of the Voigt model is established, by combining the perturbation analysis and the Laplace transformation. Degenerating into the case of Newtonian model, our Boussinesq-type equations are equivalent to those of Liu and Chan (2007), while the term indicating mud influence is greatly simplified. Based on the equations, the attenuation of solitary waves is studied. An evolution equation of wave amplitude is obtained and the development of mud velocity profiles is discussed. The modal analysis shows that the first mode always dominates mud dynamics. The results are also compared with those of the Maxwell model.