Sudden changes in a potential flow with a free surface due to impact

The impact of a region of incompressible fluid is modelled by considering the finite change that occurs in the velocity (and hence in the velocity potential) during the short time Δt of impact. The sudden switch from the initial to the final velocities is characterized by a function of time which is found and shown to be asymptotic to Heaviside's function as Δt tends to zero. The pressure field, at each point in space, is consequently a transition between two different pressures superimposed on a ‘spike’ of high pressure and of duration Δt, during impact. An appropriate boundary-value problem is posed which enables us to calculate the changes in the fields of potential, velocity and pressure. The work takes into account nonlinear terms, which have previously been neglected in the traditional theory of pressure impulse.