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INVISCID AND VISCOUS MODELS OF AXISYMMETRIC FLUID JETS OR PLUMES

Published online by Cambridge University Press:  12 November 2012

NICHOLAS A. LETCHFORD
Affiliation:
School of Mathematics and Physics, University of Tasmania, Private Bag 37, Hobart, Tasmania 7001, Australia (email: [email protected])
LAWRENCE K. FORBES*
Affiliation:
School of Mathematics and Physics, University of Tasmania, Private Bag 37, Hobart, Tasmania 7001, Australia (email: [email protected])
GRAEME C. HOCKING
Affiliation:
School of Chemical and Mathematical Sciences, Murdoch University, 90 South Street, Murdoch, Western Australia 6150, Australia (email: [email protected])
*
For correspondence; e-mail: [email protected]
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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.

MSC classification

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2012

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