Numerical investigation of air-water interaction in breaking waves

The air water interaction taking place during the breaking of free surface waves is investigated numerically. The numerical model is based on a Navier Stokes solver for a single, incompressible, fluid with variable properties. Density and viscosity jumps, as well as surface tension forces, are spread over a small region about the interface. The free surface is captured through a Level-Set technique, i.e. it is located as the zero level-set of a signed distance from the interface. The model is used to simulate the evolution of periodic wave trains of different initial amplitudes and breaking occurs for sufficiently large initial steepness. The Weber number of the simulations refers to waves of 30 cm wavelength. In order to reduce the computational effort, the Reynolds number of the simulations is an order of magnitude smaller than the real one for water waves of the same wavelength. Also, at the present stage of the study, results are limited to two-dimensional flows. It is shown that the low Reynolds number and the two-dimensional assumptions, although rather strong, do not significantly affect the solution up to about half wave period after the breaking onset. Several aspects of the resulting flow in air and water are analyzed. Particular attention is devoted to the vertical transfer of the momentum and to the circulation and vorticity field generated by the air water interaction. The fragmentation processes of air ligaments and sprays into bubbles and drops are described. It is shown that strong rotating structures are generated by the topological change of the interface and the vorticity associated to such structures is dissipated by viscous effects in a next stage. Quantitative estimates of bubbles and drops are provided. A careful analysis is conducted aimed at evaluating the limits of the numerical model in representing small bubbles or drops. For one condition, several simulations are carried out by introducing a shift, expressed as a fraction of the grid cell, in the initial free surface profile. Due to the strong nonlinearity of the process, relevant differences characterize the solutions after the breaking onset and an ensemble average among the simulations is established to derive some statistical information.