Numerical Study Of Wave Propagating And Breaking Over A Muddy Seabed

Wave propagating and breaking over the muddy coast is of great importance to thesediment transport, pollutant dispersion and shoreline changes. Conducting a study onsuch an issue has important practical value. A coupled numerical model is developedhere in which the dynamic interaction between water wave and mud is considered.Simulation of water wave propagating and breaking over the muddy seabed isperformed to obtain a deep understanding of the physical problem.Based on the incompressible viscous theory, the model is established byconsidering water and mud as two viscous fluids with large density and viscositydifference. Large eddy simulation is used to deal with the turbulence. The water surfaceand the water-mud interface are captured by the coupled Level Set and VOF (CLSVOF)method. This method overcomes the disadvantanges of Level Set method in which themass is not conserved and VOF method in which the phase function is not continuous.The numerical method is based on the projection method. Time integration and spacialdiscretization have second-order accuracy. The programis parallelized through domaindecomposition and including of MPI library functions. Attenuationof interfacial wavebetween two fluids and wave breaking over the rigid bottom are simulated to validatethe code.Study of wave propagation over the muddy seabed is performed based on thenumerical model. We consider wave propagation over the muddy seabed of differentproperties and water wave of different wave-length propagation over the same muddyseabed. It is shown that, wave decays quickly over the muddy seabed.Increasingdensityand viscosity of mud, the decay rate of water wave first increases and then decreases,the amplitude of water-mud interface always decreases, and the phase differencebetween the interfacial wave and the water wave becomes larger. Wave-length is also akey factor in the wave-mud problem. Long wave tends to lose more energy due to thebottom effect;correspondinglythe amplitude of water-mud interface is also larger. Wealso investigatethe work done by the pressure at the water-mud interface and the viscousdissipation in the mud, as they are related to the mechanism of wave attenuation.Investigations on wave breaking over the muddy seabed are rare compared with breaking over the rigid bottom. Here we perform numerical simulation of wavebreaking over the muddy seabed and compare the results with breaking over the rigidbottom. With changing the viscosity of mud, the depth of mud and the initialwave slope,we focus on the wave breaking process, the corresponding response of water-mudinterface, time history of energy, the effect of viscous and turbulent dissipation. Resultsshow that, as mud exists the inception of wave breaking is delayed and the intensity ofbreaking is weakened. With the increase of the initial wave slope, wave breaking aremore violent and the amplitude of water-mud interface decays quickly.Dissipation oftotal energy is shown to have very different rates before, during and afterbreaking. Before and after breaking, the viscous and turbulent dissipation is themain reason of energy decay; During breaking, work done against the buoyancyto entrain the air also dissipates large amount of energy.