Direct numerical simulation and large-eddy simulation are developed to investigate water waves propagating over viscous fluid mud at the bottom, with a focus on the study of wave breaking case. In the simulations, the water surface and the water–mud interface are captured with a coupled level-set and volume-of-fluid method. For non-breaking water waves of finite amplitude, it is found that the overall wave decay rate is in agreement with the existing linear theory. For breaking water waves, detailed description of the instantaneous flow field is obtained from the simulation. The time history of the total mechanical energy in water and mud shows that during the early stage of the wave breaking, the energy decays slowly; then, the energy decays rapidly; and finally, the decay rate of energy becomes small again. Statistics of the total mechanical energy indicates that the mud layer reduces the wave breaking intensity and shortens the breaking duration significantly. The effect of mud on the energy dissipation also induces a large amount of energy left in the system after the wave breaking. To obtain a better understanding of the underlying mechanism, energy transport in water and mud is analyzed in detail. A study is then performed on the viscous dissipation and the energy transfer at the water–mud interface. It is found that during the wave breaking, the majority of energy is lost at the water surface as well as through the viscous dissipation in mud. The energy and viscous dissipation in mud and the energy transfer at the water–mud interface are strongly affected by the wave breaking at the water surface.

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Available online xxxxKeywords: Two-layer system Well-balanced model Nonconservative 2LSWE HLL A robust and well-balanced numerical model is developed for solving the two-layer shallow water equations based on the approximate Riemann solver in the framework of finitevolume methods. The HLL (Harten, Lax, and van Leer) solver is employed to calculate the numerical fluxes. The numerical balance between the flux gradient and the source terms is achieved by using a balance-reformulation method. To obtain exactly the lake-atrest solutions as the water depth is chosen as the conserved variable for the continuity equations, a modified HLL flux formulation is proposed for mass flux calculations. Several numerical tests used to validate the performance of the developed numerical model. The results show that the developed model is accurate, well balanced, and that it predicts no oscillations around large gradients.

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