Computations for a nonlinear theory of fluid pressure impulse

During the impact of an ideal fluid on an impermeable surface, the velocity field undergoes a sudden change. For an irrotational flow the sudden chang e Q in the velocity potential is a harmonic function which satisfies a line ar boundary condition on the solid surface of impact. But Q satisfies a non linear boundary condition on the free surface position at the instant of im pact. Computations are presented which accurately solve the boundary-value problem for Q in a region of fluid which describes the impact of a water wa ve on to a section of vertical wall. The fluid has a horizontal free surfac e at impact. The nonlinear term in the free-surface boundary condition poss esses a coefficient epsilon. The results show that the nonlinear term incre ases the speed at which fluid begins to ascend close to the wall after impa ct, but this increase tends to zero as epsilon tends to zero. The results s how that fluid impact problems can be treated effectively while neglecting the nonlinear convective terms in Euler's equations of ideal flow.