Keywords: interfacial wave, porous bed, two layer, numerical.

Fluid mud layers develop close to the seabed either by fast deposition of suspended particulate matter or by the fluidisation of recently deposited sediment layers. Some common marine pollutants such as trace metals and pesticides are known to settle and accumulate in such muds [1]. The mud layer may fluidise due to wave action and this process is known to create layers of mud with properties which are dependent on the magnitude of the induced oscillatory strain [2].

The objective of this study is to investigate the propagation of a water wave above a stratified seabed, where the layers considered to each have a different but constant density and viscosity. The upper layer represents water and the lower layer a more dense and viscous fluid mud, underlain by a rigid porous domain. The height of the surface wave is specified and the initial characteristics of the forced interfacial wave and the depths of the mud layers are determined as a function of the imposed oscillatory wave characteristics. The viscous attenuation of the wave due to the combined effects of the wave interaction with the porous seabed, damping within the fluid layers, and damping at the interface of the two fluids is considered numerically using an Arbitrary Lagrangian-Eulerian method. The incompressible Navier-Stokes equations in two-dimensions are used to describe the fluid motion within the two homogeneous fluid layers. The fluid flow is coupled to the saturated porous seabed beneath using the Brinkman equations.

The model results are discussed and compared with previous analytical approximations. It is shown that the magnitude of the wave energy dissipation is determined by the depths of the two fluid layers.

1

H.-T. Chou, J.R. Hunt, M. A. Foda, "Fluidization of marine mud by waves", Marine Poll. Bulletin, 23, 1991. doi:10.1016/0025-326X(91)90653-A

2

M.A. Foda, "Role of wave pressure in bedload sediment transport", J. Waterway, Port, Coastal and Ocean Eng.-ASCE, 129, 6, 243-249, 2003. doi:10.1061/(ASCE)0733-950X(2003)129:6(243)

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