Abstract
A numerical model for the interaction between waves and muddy seabed is developed, in which the motion of the movable mud and the motion of water are solved simultaneously. The governing equations for both water and the mud are the continuity equation and the equations of motion for incompressible fluids. Water is treated as a Newtonian fluid, while a visco-elastic-plastic model is used to describe the rheology of the mud. Both the interface between water and the mud and the free water surface are traced by the VOF (Volume of Fluid) method. The numerical method is based on the well-known SMAC method. The numerical model is applied to simulate wave propagation over a muddy slope, and the numerical results are in reasonable agreement with the experimental data. The present model is proved better performance than the traditional analytic model in case that topography change is not negligible.
Highlights
The existence of fluid mud has been widely reported at muddy coasts or estuaries
In order to validate the wave model, the model is applied to modeling wave over a submerged bar and the simulated results are compared with the observations of experiment carried out by Beji and Battjes (1993)
A numerical model for the interaction between waves and muddy bed has been developed, which ignores the exchange of sediment between the water layer and the mud layer and treat water and the movable mud as two unmixable fluids
Summary
Fluid mud can be transported by gravity and by waves. A number of analytic studies have been carried out on the interaction between waves and a muddy bed. In the pioneering work of Gade (1958), attenuation of shallow water waves was studied based on a two-layer model, in which the upper layer, or the water, was treated as an inviscid fluid, while the lower layer, or the mud, was assumed to be a viscous fluid. Maa and Mehta (1990) argued that the variation of the mud properties in the vertical direction can not be neglected and developed a multi-layer model. Considering the movable mud layer on seabed is thin, a two-fluid Stokes boundary layer model was developed by Ng (2000)
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