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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 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Quarterly Journal of Mechanics and Applied Mathematics Oxford University Press

Computations for a Nonlinear Theory of Fluid Pressure Impulse

Abstract

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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