# 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.

/lp/oxford-university-press/computations-for-a-nonlinear-theory-of-fluid-pressure-impulse-Dr7B0P10Fr

### How DeepDyve Works

Spend time researching, not time worrying you’re buying articles that might not be useful.

### Stay up to date

It’s easy to organize your research with our built-in tools.

### Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from Springer, Elsevier, Nature, IEEE, Wiley-Blackwell and more.

All the latest content is available, no embargo periods.

### Simple and Affordable Pricing

14-day free trial. Cancel anytime, with a 30-day money-back guarantee.

### Monthly Plan

• Personalized recommendations
• Print 20 pages per month
• 20% off on PDF purchases