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RAYLEIGH–TAYLOR INSTABILITIES IN AXI-SYMMETRIC OUTFLOW FROM A POINT SOURCE

Part of: Hydrodynamic stability

Published online by Cambridge University Press:  05 July 2012

LAWRENCE K. FORBES
LAWRENCE K. FORBES*
Affiliation:
School of Mathematics and Physics, University of Tasmania, Private Bag 37, Hobart, Tasmania 7001, Australia (email: [email protected])
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Abstract

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This paper studies outflow of a light fluid from a point source, starting from an initially spherical bubble. This region of light fluid is embedded in a heavy fluid, from which it is separated by a thin interface. A gravitational force directed radially inward toward the mass source is permitted. Because the light inner fluid is pushing the heavy outer fluid, the interface between them may be unstable to small perturbations, in the Rayleigh–Taylor sense. An inviscid model of this two-layer flow is presented, and a linearized solution is developed for early times. It is argued that the inviscid solution develops a point of infinite curvature at the interface within finite time, after which the solution fails to exist. A Boussinesq viscous model is then presented as a means of quantifying the precise effects of viscosity. The interface is represented as a narrow region of large density gradient. The viscous results agree well with the inviscid theory at early times, but the curvature singularity of the inviscid theory is instead replaced by jet formation in the viscous case. This may be of relevance to underwater explosions and stellar evolution.

Keywords

interfaceinstabilitycurvature singularityRayleigh–Taylor flowspectral methodsspherical coordinatesBoussinesq approximationvorticityone-sided outflows

MSC classification

Secondary: 76E17: Interfacial stability and instability
Type
Research Article
Information
The ANZIAM Journal , Volume 53 , Issue 2 , October 2011 , pp. 87 - 121
Copyright
Copyright © Australian Mathematical Society 2012

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