Blunt-body impact on a compressible liquid surface

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Abstract
In this paper we are concerned with the unsteady plane liquid motion due to the penetration of a blunt undeformable contour through the free surface. Initially the liquid is at rest, and the contour touches its free surface at a single point. At the initial stage of the process the liquid motion is described within the framework of the acoustic approximation. It is known that, just behind the shock front which is generated under the impact, the liquid motion does not depend on the presence of the free surface for all time. The pressure distribution and the velocities of liquid particles inside this region are calculated analytically for an arbitrary contour. It is shown that liquid motion close to the contact points just before the shock wave escapes onto the free surface is self-similar; the singularity of the pressure is analysed. The focusing of the shock wave generated by the impact of a body with a shallow depression in the front surface is discussed.

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