Pressure analysis in nonlinear waves by revisiting the breaking wave onset

Abstract

Breaking waves are numerically simulated by solving the two dimensional nonlinear free surface boundary conditions in potential theory. Onset of breaking wave is determined for two configurations: A focused wave in intermediate depth and a dambreaking flow leading to a soliton. Two criteria are identified: first, a kinematic criterion follows from the ratio of the horizontal velocity at the crest to the phase velocity; second, a dynamic criterion is formulated in terms of the vertical pressure gradient. Thresholds of these criteria are proposed in the literature. For the two configurations studied here, it is shown that these thresholds are not universal but they are reasonable estimates of the onset of breaking wave. To facilitate this study, the Hessian matrix of the pressure is analyzed. It is shown that there exists a continuous curve that links the crest of the wave to the sea bottom. This line follows from the colinearity of the pressure gradient and one of the two eigenvectors of the Hessian matrix. The analysis of the pressure, its gradient and its second derivatives along this line gives more insights into the definition of the thresholds associated to the onset of breaking wave.