Numerical analysis of the momentum transfer induced by breaking waves

The flow generated by the breaking of free surface waves is numerically simulated with the aim of investigating the vertical transfer of horizontal momentum and the energy decay. The study is carried out through a two-fluids Navier-Stokes solver which uses a Level-Set technique for the interface capturing. Two different flow conditions are considered which are the purely unsteady flow induced by the evolution to breaking of a rather steep water wave, and the flow generated by a quasi-steady breaker produced by a hydrofoil towed beneath the free surface. The former problem is studied in a computational domain with periodic boundary conditions at the two sides. The mean and fluctuating components of the flow are distinguished via an ensemble average of a set of solutions obtained by introducing a random phase shift to the initial conditions. Results are presented in terms of the mean free surface shape, averaged air/water fraction, and velocity and vorticity fields. According to previous studies, it is found that, soon after the first jet impact, the kinetic energy decays like t-1 and most of the initial energy is dissipated within few wave periods. The flux of horizontal momentum through horizontal lines lying at different depths is calculated. It is found that the contribution of the mean flow to the downward transfer of the momentum progressively diminishes with increasing the depth whereas the contribution of the fluctuations is characterized by a maximum located about the top of the vortex generated during the impact process. In the quasi-steady wave breaking flow the mean and fluctuating components are derived through a time average of the solution. Comparisons with experimental measurements in similar conditions are established. The mean velocity profiles and the distribution of the Reynolds stresses indicate that a shear layer develops at the breaker toe, characterized by a large growth rate. The contributions of the mean and fluctuating components to the downward transfer of the horizontal momentum are evaluated and differences with respect to those found for the unsteady case are discussed. For both flow conditions a dimensionless energy decay rate is estimated and compared with corresponding estimates available in literature.