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The temporal stability of a developing jet: a model problem

Published online by Cambridge University Press:  17 February 2009

Jillian A. K. Stott  and
James P. Denier
Jillian A. K. Stott
Affiliation:
School of Mathematics, The University of NSW, PO Box 1, Kensington, NSW 2033, Australia.
James P. Denier
Affiliation:
School of Mathematics, The University of NSW, PO Box 1, Kensington, NSW 2033, Australia. Now at Department of Applied Mathematics, University of Adelaide, SA 5005, Australia.
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Abstract

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The temporal instability of a developing swirling incompressible jet is considered. The jet development (in the streamwise direction) is modelled by combining a near-field and far-field approximation to the jet velocity profile into a one parameter family of basic velocity fields. The single parameter in the jet velocity field then allows us to model the radial spreading of the jet and the decay of swirl observed experimentally. Two distinct modes of instability of this model profile are found. The first is that found from a stability analysis of a fully developed swirling jet in the far field whilst the second is relevant to a “top-hat” jet with an imposed rigid body rotation. We demonstrate that the effect of azimuthal swirl is to destabilise both modes of instability. Additionally our results suggest that the near-nozzle modes of instability will dominate; indeed the growth rates of these modes are significantly larger than those found from previous studies of a fully developed jet in the far-field region.

Type
Research Article
Information
The ANZIAM Journal , Volume 37 , Issue 2 , October 1995 , pp. 235 - 252
Copyright
Copyright © Australian Mathematical Society 1995

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