Modeling of the Turbulence in the Water Column under Breaking Wind Waves

Abstract

Past studies have shown that there is a wave-enhanced, near-surface mixed-layer in which the dissipation rate is greater than that derived from the “law of the wall”. In this study, turbulence in water columns under wind breaking waves is investigated numerically and analytically. Improved estimations of dissipation rate are parameterized as surface source of turbulent kinetic energy (TKE) for a more accurate modelling of vertical profile of velocity and TKE in the water column. The simulation results have been compared with the experimental results obtained by Cheung and Street (1988) and Kitaigorodskii et al. (1983), with good agreement. The results show that the numerical full model can well simulate the near-surface wave-enhanced layer and suggest that the vertical diffusive coefficients are highly empirical and related to the TKE diffusion, the shear production and the dissipation. Analytical solutions of TKE are also derived for near surface layer and in deep water respectively. Near the surface layer, the dissipation rate is assumed to be balanced by the TKE diffusion to obtain the analytical solution; however, the balance between the dissipation and the shear production is applied at the deep layer. The analytical results in various layers are compared with that of the full numerical model, which confirms that the wave-enhanced layer near the surface is a diffusion-dominated region. The influence of the wave energy factor is also examined, which increases the surface TKE flux with the wave development. Under this region, the water behavior transits to satisfy the classic law of the wall. Below the transition depth, the shear production dominantly balances the dissipation.