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Traditional turbulence models are derived for single-phase flow. Extension ofthe family of two-equation turbulence models for two-phase flow is obtained viascaling the transport equations by the density. In the special case oftwo-phase flow with a sharp interface, jump conditions exist. Two types of jumpconditions are found: (1) jump in the partial differential equation (PDE)physical quantities such as density and viscosity and (2) jump in theturbulence frequency. We first derive and clarify the jump in the equations.The jump in the turbulence frequency is proportional to the kinematic viscosityratio, which is approximately $10$ in the case of air-water. Then a new field,the inverse turbulence area, is considered to model the turbulence effectsinstead of the turbulence frequency. For the system of air and water, theeffect of the jump of the kinematic viscosity is always greater than the effectarising from the jump of velocity gradient. This approximation leads to theassumption of a continuous inverse turbulence area scale. Validation versusexperimental measurements from the literature is then presented to demonstratethe improvement of the model. In particular, the wave breaking phenomenon issimulated in two conditions: spilling and plunging wave breakers. The proposedmodel shows its ability to predict the turbulence in the surf zone accurately.Finally, it explains the low values of the time-averaged turbulent kineticenergy in the surf zone which is caused by the increase of the turbulencefrequency in the air.

On computing the jump condition of the dissipation rate in the two-equation turbulence models for two-phase flow and application to air-water waves