Abstract
Abstract
Highlights
The Cauchy–Poisson problem is classical in fluid mechanics and applied mathematics
We have investigated a nonlinear Cauchy–Poisson problem where the flow is caused entirely by an impulsive surface pressure which puts the initially horizontal surface instantaneously into motion
Even though the net momentum is vertical, most surface particles will be put into tangential initial motion, because of the tangential derivative of the surface pressure impulse
Summary
The Cauchy–Poisson problem is classical in fluid mechanics and applied mathematics. This pioneering initial-value problem for water waves is described in the textbook by Lamb (1932, pp. 384–398). The early time span of a gravitational time unit will be decisive for the further nonlinear process This is known from two theoretical studies on the present class of Cauchy–Poisson problem, where a surface pressure is turned on to work on the initially horizontal surface of a semi-infinite fluid. Longuet-Higgins & Dommermuth (2001) realized that a similar model could be interesting for investigating the highest transient waves, which they did They applied an instantaneous pressure impulse instead of the surface pressure of long duration studied by Saffman & Yuen (1979). The conventional way of modelling incompressible slamming problems (water impact) is to give the forced impulsive motion of a body entering a liquid with an initially free horizontal surface, and compute the resulting flow and the impact pressure forces that it generates on the body. We will show and compare two analytical and one numerical approach to the same strongly nonlinear problem, and investigate in detail how the analytical solutions fail when the free-surface nonlinearity becomes too strong
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