Idealized numerical simulation of breaking water wave propagating over a viscous mud layer

Abstract

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.

Three-Dimensional Numerical Simulations of Aerated Vortex Filaments Under Plunging Breaking Waves

“…This somewhat artificial wave breaking configuration has already been documented in several previous studies and proved to be effective at simulating all types of breaking waves (Abadie et al 1998;Chen et al 1999;Lubin et al 2006;Iafrati 2009;Hu et al 2012).…”

Numerical Study on the Generation and Transport of Spume Droplets in Wind over Breaking Waves

“…Equations (8) and (9) are coupled using the method of Sussman and Puckett [55]. A more detailed description of the numerical method is given in Liu [57], Hu et al [61] and Yang et al [67].…”

“…Periodic boundary conditions are used in the x-and y-directions. We note here that the use of the periodic boundary condition is a common practice in simulations of breaking waves [58][59][60][61][62][63][64], because the non-periodic condition would substantially increase the computational cost. The no-slip condition is imposed at the bottom.…”

“…The initial flow field is fully-developed wind turbulence over prescribed steep waves. Following the practice of many previous two-fluid numerical simulations of wave breaking [58][59][60][61][62][63][64], the initial wave geometry is given by the analytical solution of the third-order Stokes wave as:…”

Instability of the interface in two-layer flows with large viscosity contrast at small Reynolds numbers

“…Hence, its Bingham property is not obvious, and it can be treated as a Newtonian fluid [5]. As a matter of fact, there are a lot of papers taking the fluid mud as Newtonian fluid in theoretical analysis or numerical simulation [6][7][8][9][10][11]. The cohesive fine sediments make fluid mud a structural integrity rather than a mixture of isolated particles.…”