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The Quarterly Journal of Mechanics and Applied Mathematics 2001 54(4):585-598; doi:10.1093/qjmam/54.4.585
© 2001 by Oxford University Press
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Computations for a Nonlinear Theory of Fluid Pressure Impulse

M. J. Cooker1 and J.-M. Vanden-Broeck1

( 1 School of Mathematics, University of East Anglia, Norwich NR4 7TJ )

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


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