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Bubbles, breaking waves and hyperbolic jets at a free surface

Published online by Cambridge University Press:  20 April 2006

M. S. Longuet-Higgins
M. S. Longuet-Higgins
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, and Institute of Oceanographic Sciences, Wormley, Surrey
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Abstract

Experiments have shown that bubbles approaching an air–water interface give rise to axisymmetric jets projected upwards into the air. Similar jets occur during the collapse of cavitation bubbles near a solid surface. In this paper we show that such jets are well modelled by a Dirichlet hyperboloid, a hyperbolic form of the better-known ellipsoid. The vertex angle of the hyperboloid is calculated as a function of time and found to agree with the observations of Blake & Gibson (1981) and others.

The jet is initiated, according to this model, when the vertex angle passes through 2 arctan √2, or 109·47°, at which instant the fluid accelerations become large. This compares with a vertical angle of 90° in the corresponding two-dimensional flow.

Further experiments demonstrate that an axisymmetric standing wave, when driven beyond its maximum amplitude, can break by throwing up a jet of the same hyperbolic form. Hyperbolic jets may occur commonly in free-surface flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 127 , February 1983 , pp. 103 - 121
Copyright
© 1983 Cambridge University Press

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