Modelling of surface waves breaking effects in the ocean upper layer

Abstract

In this paper, we have studied the general dynamic structure of the turbulent upper layer produced by wave breaking and turbulent diffusion of wave kinetic energy. The turbulent model is of the k-ε group model. The TKE budget contains an extra term, which describes the turbulent diffusion of wave kinetic energy. We suggest a parameterization of the momentum flux and the energy flux induced by the wave breaking. The analysis is focused at the upper part of the Ekman layer where the constant friction approach is valid. It is shown that this layer is formed of three sublayers. The nearest layer to the ocean surface is the wave-turbulent sublayer. The turbulent energy production by the wave breaking significantly exceeds the mean shear effect, and the turbulent diffusion of the wave kinetic energy dominates in the range of depths where the wave motion continues to be vigorous. Below this layer, the wave effect does not play a significant role because the turbulent diffusion of turbulent kinetic energy begins to exceed the wave effect in the TKE budget. However, the turbulence of this layer influences the dynamics of the entire Ekman layer beneath. Below the wave-turbulent diffusive layer, there is a transitional turbulent diffusive layer where the turbulent diffusion still exceeds the mean shear contribution in the TKE budget but the wave motion effect becomes insignificant. The source of turbulence in this layer is the turbulent kinetic energy flux from the upper wave-turbulent layer. The turbulent kinetic energy and the dissipation rate decay with depth following power laws. Theoretical prediction is consistent with data observed in the ocean. Following after the transition turbulent diffusive layer, there is a layer where the mean shear production of turbulent energy dominates. In terms of the classic steady turbulent boundary layer problem, this layer, in steady or quasi-steady cases, corresponds to the logarithmic turbulent sublayer where the “wall turbulence” laws are valid. However, all turbulent characteristics are controlled by the wave breaking mechanism and the turbulence dynamics in the wave-turbulent layer and the turbulent diffusive layer. We may conclude that the suggested model gives an adequate description of the natural ocean turbulence for the constant friction layer of the upper ocean.