Some aspects of the pressure field preceding the onset of critical jets in a breaking wave
Résumé
We consider in this article two-dimensional nonlinear free surface motions in potential theory. There are situations where the onset of critical jet along a free surface can be predicted by analyzing the temporal and spatial variation of the pressure itself and its successive derivatives. In particular, when a local maximum of pressure appears close enough to a free surface where the pressure vanishes, it is expected a great pressure gradient at the free surface and consequently a large Lagrangian acceleration. The present analysis examines this phenomenon. This analysis is facilitated after identifying a line along which the pressure gradient is parallel to one of the eigenvectors of the Hessian matrix of the pressure. In a standard overturning crest, this line connects the tip of the crest to the bottom of the tank in which the flow is simulated. The analysis of its time evolution gives much information into the onset of critical jets. Other types of critical jet can also appear when a region of positive Gaussian curvature of the pressure suddenly grows in the vicinity of the free surface.