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Inviscid Swirling Flows and Vortex Breakdown

Buntine, J. D. and Saffman, P. G. (1995) Inviscid Swirling Flows and Vortex Breakdown. Proceedings of the Royal Society of London. Series A, Mathematical, Physical and Engineering Sciences, 449 (1935). pp. 139-153. ISSN 0962-8444.

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The steady axisymmetric Euler flow of an inviscid incompressible swirling fluid is described exactly by the Squire-Long equation. This equation is studied numerically for the case of diverging flow to investigate the dependence of solutions on upstream, or inlet, and downstream, or outlet, boundary conditions and flow geometry. The work is performed with a view to understanding how the phenomenon of vortex breakdown occurs. It is shown that solutions fail to exist or, alternatively, that the axial flow ceases to be unidirectional, so that breakdown can be inferred, when a parameter measuring the relative magnitude of rotation and axial flow (the Squire number) exceeds critical values depending upon the geometry and inlet profiles. A 'quasi-cylindrical' simplification of the Squire-Long equation is compared with the more complete Euler model and shown to be able to account for most of the latter's behaviour. The relationship is examined between 'failure' of the quasi-cylindrical model and the occurrence of a 'critical' flow state in which disturbances can stand in the flow.

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Additional Information:© 1995 The Royal Society. Received 19 April 1994; accepted 19 October 1994. This work was supported by the Department of Energy Grant No. DE-FG03-89ER25073. The authors thank Professor D. I. Pullin, Dr S. J. Cowley, Professor D. W. Moore and Professor J. M. Lopez for constructive criticism. Dr Cowley has independently considered questions similar to those presently investigated.
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Department of Energy (DOE)DE-FG03-89ER25073
Issue or Number:1935
Record Number:CaltechAUTHORS:20141217-153936617
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Official Citation:Inviscid Swirling Flows and Vortex Breakdown J. D. Buntine and P. G. Saffman Proceedings: Mathematical and Physical Sciences Vol. 449, No. 1935 (Apr. 8, 1995) , pp. 139-153 Published by: The Royal Society Stable URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:52993
Deposited By: Tony Diaz
Deposited On:17 Dec 2014 23:59
Last Modified:03 Oct 2019 07:46

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