Properties of the pressure field in highly nonlinear free surface flows with critical jet

In this note we examine fluid violent kinematics in a plunging breaker. The fluid motion is computed in the frame of the potential flow theory. The fluid kinematics is basically generated by forcing the motion of a rectangular tank, starting from rest. When a sufficient level of energy is injected in the fluid, the free surface has highly nonlinear behavior, here a plunging breaker. In the vicinity of the main tip crest, a sharp corner (cusp) appears along the surface of the barrel. The appearance of this critical jet is described and discussed in terms of the spatial and temporal variations of the pressure field. In the present case a local pressure maximum is captured that follows a continuous decreasing pressure gradient in a region of positive Gaussian curvature of the pressure. It is also shown that, at the free surface before the appearance of the critical jet, there is a strong correlation between the change of sign of the Gaussian curvature of the pressure on the one hand and the radius of curvature of the free surface profile on the other hand.