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Trapping of air in impact between a body and shallow water

Published online by Cambridge University Press:  25 September 2008

A. A. KOROBKIN ,
A. S. ELLIS  and
F. T. SMITH
A. A. KOROBKIN
Affiliation:
Lavrentyev Institute of Hydrodynamics, Novosibirsk, 630090, Russia
A. S. ELLIS
Affiliation:
Dept. of Mathematics, UCL, Gower Street, London WC1E 6BT, UK.
F. T. SMITH
Affiliation:
Dept. of Mathematics, UCL, Gower Street, London WC1E 6BT, UK.
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Abstract

Near-impact behaviour is investigated for a solid body approaching another solid body with two immiscible incompressible viscous fluids occupying the gap in between. The fluids have viscosity and density ratios which are extreme, the most notable combination being water and air, such that either or both of the bodies are covered by a thin film of water. Air–water interaction and the commonly observed phenomenon of air trapping are of concern in the presence of the two or three thin layers and one or two interfaces. The subcritical regime is of most practical significance here and it leads physically to the effect of inviscid water dynamics coupling with a viscous-dominated air response locally. This physical mechanism induces touchdown (or an approach to touchdown), which is found to occur in the sense that the scaled air-gap thickness shrinks towards zero within a finite scaled time according to analysis performed hand in hand with computation. A global influence on the local touchdown properties is also identified. Comparisons with computations prove favourable. Air trapping is produced between two touchdown positions, at each of which there is a pressure peak; an oblique approach would not affect the finding unless the approach itself is extremely shallow. The mechanism of air–water interaction leading to air trapping is suggested as a quite wide-ranging result.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 611 , 25 September 2008 , pp. 365 - 394
Copyright
Copyright © Cambridge University Press 2008

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