Analysis of wave breaking events generated as a result of a modulational instability

The evolution of modulated wave systems is investigated numerically. The study is conducted by using two different approaches. A fully nonlinear potential solver is adopted to study the wave dynamics until the instability develops. Hence, the solution is transferred to a more expensive two-fluids Navier-Stokes solver which describes the breaking process. The study is aimed at analyzing the breaking induced by the modulational instability. To this aim, a modulated wave train is initialized by adding two sideband components. For initial steepnesses larger than a threshold value, the steepening process induced by the modulation causes the wave to break. The main interest of the study is in the amount of energy dissipated by the breaking occurrence and how it changes with the characteristics of the initial spectrum. Results are provided in terms of free surface profiles, velocity and vorticity fields, energy contents and viscous dissipation. Solutions in both air and water are presented. The limits of the numerical models are analyzed and discussed, and results obtained on different discretizations are compared. According to previous findings, the breaking is found to occur with a period which is about twice the period of the fundamental wave component. Differently from what happens in the case of linear superposition, the dissipation of the energy takes place in steps, as a result of the modulation/demodulation process. Of particular interest is the role played by the dissipation in air which, in the modulational instability case, is found to dominate over the dissipation in water.