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INVISCID AND VISCOUS MODELS OF AXISYMMETRIC FLUID JETS OR PLUMES

Part of: Incompressible viscous fluids

Published online by Cambridge University Press:  12 November 2012

NICHOLAS A. LETCHFORD ,
LAWRENCE K. FORBES  and
GRAEME C. HOCKING
NICHOLAS A. LETCHFORD
Affiliation:
School of Mathematics and Physics, University of Tasmania, Private Bag 37, Hobart, Tasmania 7001, Australia (email: Larry.Forbes@utas.edu.au)
LAWRENCE K. FORBES*
Affiliation:
School of Mathematics and Physics, University of Tasmania, Private Bag 37, Hobart, Tasmania 7001, Australia (email: Larry.Forbes@utas.edu.au)
GRAEME C. HOCKING
Affiliation:
School of Chemical and Mathematical Sciences, Murdoch University, 90 South Street, Murdoch, Western Australia 6150, Australia (email: G.Hocking@murdoch.edu.au)
*
✉For correspondence; e-mail: Larry.Forbes@utas.edu.au
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Abstract

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The vertical rise of a round plume of light fluid through a surrounding heavier fluid is considered. An inviscid model is analysed in which the boundary of the plume is taken to be a sharp interface. An efficient spectral method is used to solve this nonlinear free-boundary problem, and shows that the plume narrows as it rises. A generalized condition is also introduced at the boundary, and allows the ambient fluid to be entrained into the rising plume. In this case, the fluid plume first narrows then widens as it rises. These features are confirmed by an asymptotic analysis. A viscous model of the same situation is also proposed, based on a Boussinesq approximation. It qualitatively confirms the widening of the plume due to entrainment of the ambient fluid, but also shows the presence of vortex rings around the interface of the rising plume.

Keywords

fluid jetaxisymmetric flowinviscid theoryspectral methodsplumeBoussinesq approximationentrainment

MSC classification

Secondary: 76D25: Wakes and jets
Type
Research Article
Information
The ANZIAM Journal , Volume 53 , Issue 3 , January 2012 , pp. 228 - 250
Copyright
Copyright © Australian Mathematical Society 2012

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