Viscous flows in a muddy seabed induced by a solitary wave

Abstract

Liu & Chan (J. Fluid Mech.vol. 579, 2007, p. 467, hereinafter referred to as LC) derived analytical solutions for the interactions between shallow water waves and a viscous fluid seabed. In this paper we present a set of new experimental data on the solitary-wave-induced flows in a viscous muddy seabed so as to validate LC's theory and the approximations employed. In the experiments a clear silicone fluid was used as the viscous mud and particle image velocimetry was employed to measure the velocity field inside the viscous mud. The shear stress along the bottom of the mud bed and the displacement of the water--mud interface were also deduced from data. Experimental results showed excellent agreement with the theoretical solutions. Additional analyses were performed to show that the ratio of the muddy seabed thickness to the corresponding bottom boundary-layer thickness,$\dbar$, plays an important role in characterizing mud flow regimes. When$\dbar\,{\leq}\,1$, the vertical profile of the horizontal velocity in the mud bed can be parameterized as a parabola. On the other hand, when$\dbar\,{\gg}\,1$, the velocity profile appears as a plug flow above a thin viscous layer. When$ \dbar\,{\sim}\,O(1)$, the flow patterns are more complex than the other two regimes and flow reversal can occur inside the viscous mud bed.