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EXACT SOLUTIONS FOR INTERFACIAL OUTFLOWS WITH STRAINING

Part of: Incompressible inviscid fluids

Published online by Cambridge University Press:  05 June 2014

LAWRENCE K. FORBES  and
MICHAEL A. BRIDESON
LAWRENCE K. FORBES*
Affiliation:
School of Mathematics and Physics, University of Tasmania, Private Bag 37, Hobart, Tasmania, Australia email [email protected], [email protected]
MICHAEL A. BRIDESON
Affiliation:
School of Mathematics and Physics, University of Tasmania, Private Bag 37, Hobart, Tasmania, Australia email [email protected], [email protected]
*
✉[email protected]
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Abstract

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In models of fluid outflows from point or line sources, an interface is present, and it is forced outwards as time progresses. Although various types of fluid instabilities are possible at the interface, it is nevertheless of interest to know the development of its overall shape with time. If the fluids on either side are of nearly equal densities, it is possible to derive a single nonlinear partial differential equation that describes the interfacial shape with time. Although nonlinear, this equation admits a simple transformation that renders it linear, so that closed-form solutions are possible. Two such solutions are illustrated; for a line source in a planar straining flow and a point source in an axisymmetric background flow. Possible applications in astrophysics are discussed.

Keywords

closed-form solutionhydrodynamicsinterfacial fluid flowstraining flow

MSC classification

Secondary: 76B07: Free-surface potential flows
Type
Research Article
Information
The ANZIAM Journal , Volume 55 , Issue 3 , January 2014 , pp. 232 - 244
Copyright
Copyright © 2014 Australian Mathematical Society 

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