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Steady axisymmetric vortex flows with swirl and shear

Published online by Cambridge University Press:  01 October 2008

ALAN R. ELCRAT ,
BENGT FORNBERG  and
KENNETH G. MILLER
ALAN R. ELCRAT
Affiliation:
Department of Mathematics, Wichita State University, Wichita, KS 67260, USA
BENGT FORNBERG
Affiliation:
Department of Applied Mathematics, University of Colorado, Boulder, CO 80309, USA
KENNETH G. MILLER
Affiliation:
Department of Mathematics, Wichita State University, Wichita, KS 67260, USA
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Abstract

A general procedure is presented for computing axisymmetric swirling vortices which are steady with respect to an inviscid flow that is either uniform at infinity or includes shear. We consider cases both with and without a spherical obstacle. Choices of numerical parameters are given which yield vortex rings with swirl, attached vortices with swirl analogous to spherical vortices found by Moffatt, tubes of vorticity extending to infinity and Beltrami flows. When there is a spherical obstacle we have found multiple solutions for each set of parameters. Flows are found by numerically solving the Bragg–Hawthorne equation using a non-Newton-based iterative procedure which is robust in its dependence on an initial guess.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 613 , 25 October 2008 , pp. 395 - 410
Copyright
Copyright © Cambridge University Press 2008

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