A numerical study on wave-mud interaction

Presented in this paper is a numerical study on the interaction of progressive waves propagating in a body of water overlying a layer of viscous fluid mud on the bottom, with emphasis placed on the induced oscillatory motion of the water-mud interface. The fully nonlinear Navier-Stokes equations with the complete set of viscous boundary conditions are solved numerically by a finite difference method that is based on a time-dependent boundary-fitted curvilinear coordinate system, for the simulation of wave motion in the two-layer viscous fluid system. Waves of moderate wavelength are generated in the upper water layer by a numerical flap-type wavemaker. The dynamic pressure due to the surface wave is transmitted downward onto the lower layer, generating wave motion on the interface. On mimicking some reported experimental conditions, the ratio of interfacial to surface wave amplitudes is evaluated and the results are found to compare more favorably with the experimental data than the prediction by a linear theory.