Tsunami generation by a seabed deformation in the presence of a viscoelastic mud

In this work, under the assumption of linear water waves, we study tsunamis generated by a seabed deformation in the presence of a viscoelastic mud. We divide the total control volume, under study, into a water layer, which is assumed as an irrotational and inviscid flow, and a mud layer with viscoelastic properties that obeys a linear Maxwell rheological model. Considering that the fluid layers thicknesses are of the same order of magnitude and that they are much smaller than the characteristic horizontal length of the seabed deformation, we obtain a semi-analytical solution that models the evolution of the free surface elevation. For the above limits, the fluid motion in the water layer is essentially horizontal. Passive and active tsunami generation cases are analyzed. The seabed deformation is modeled as a Heaviside step function. For an active generation case, when the mud layer thickness increases, the tsunami's maximum amplitude decreases. For the passive generation case, the tsunami's maximum amplitude remains constant in a finite time interval of the same order of magnitude as the characteristic time, this phenomena does not occur for the active generation case.