Bubbles, breaking waves and hyperbolic jets at a free surface

Author:
Publisher website
Google Scholar
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.

This publication has 21 references indexed in Scilit: