Numerical study of the effects of the breaking intensity on wave breaking flows

Abstract

The flow generated by the breaking of free-surface waves of different initial steepnesses is simulated numerically. The aim is to investigate the role played by the breaking intensity on the resulting flow. The study, which assumes a two-dimensional flow, makes use of a two-fluids Navier–Stokes solver combined with a Level-Set technique for the interface capturing. The evolution of periodic wavetrains is considered. Depending on the initial steepness ϵ, the wavetrain remains regular or develops a breaking, which can be either of spilling or plunging type. From the analysis of the local strain fields it is shown that, in the most energetic phase of plunging breaking, dissipation is mainly localized about the small air bubbles generated by the fragmentation of the air cavity entrapped by the plunging of the jet. The downward transfer of the horizontal momentum is evaluated by integrating the flux of momentum through horizontal planes lying at different depths beneath the still water level. From weak to moderate breaking, increase in the breaking intensity results in growing transfer of horizontal momentum, as well as thickening of the surface layer. Beyond a certain breaking intensity, the larger amount of air entrapped causes a reduction in the momentum transferred and the shrinkage of the layer. Quantitative estimates of the amount of air entrapped by the breaking and of the degassing process are provided. A scaling dependence of the amount of air entrapped by the first plunging event on the initial steepness is found. A careful analysis of the circulation induced in water by the breaking process is carried out. It is seen that in the plunging regime the primary circulation induced by the breaking process scales with the velocity jump between the crest and the trough of the wave.The limits of the main assumptions of the numerical calculations are analysed. It is shown that up to half-wave period after the breaking onset, the Reynolds number of the simulation does not significantly affect the solution. In order to further support the findings, an estimate of the uncertainty of the numerical results is derived through several repetitions of the numerical simulation with small perturbations of the initial conditions.