Numerical simulation of breaking waves by a multi-scale turbulence model

In this paper, a two-dimensional multi-scale turbulence model is proposed to study breaking waves. The purpose of developing this model is to produce a relatively accurate model with moderate computer requirements. The free surface is tracked by the VOF technique, the log-law profile for the mean velocity is applied at the bottom. Comparing with the Reynolds-Averaged Navier-Stokes models (RANS), the present model shows improving agreement with experimental measurements in terms of surface elevations, particle velocities, wave height distributions and undertow profiles. The subgrid scale (SGS) turbulent transport mechanism is also discussed in the paper. It is found that turbulent production and dissipation are of the same order, but turbulent production is primarily located at the wavefront and above the wave trough, whereas turbulent dissipation is primarily located at the back face of a wave, indicating that in these regions, the assumption of equilibrium is not correct. Below the trough level, the local equilibrium assumption is reasonable. Turbulent convection and diffusion are of the same order at the trough level. Above the trough level, turbulent convection dominates. Under the spilling breaking wave, turbulent kinetic energy is continue to dissipate in the bore region, whereas under the plunging breaking wave, the turbulent kinetic energy is dissipated very rapidly within one wave period.