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Steady axisymmetric vortex flows with swirl and shear


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.

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C. J. Amick & L. E. Fraenkel 1988 The uniqueness of a family of steady vortex rings. Rat. Mech. Anal. 100, 207241.

Y. Fukumoto 2002 Higher-order asymptotic theory for the velocity field induced by an inviscid vortex ring. Fluid Dyn. Res. 30, 6592.

A. Lifschitz , W. H. Suters & J. T. Beale 1996 The onset of instability in exact vortex rings with swirl. J. Comput. Phys. 129, 829.

K. Mohseni & M. Gharib 1998 A model for universal time scale of vortex ring formation. Phys. Fluids 10, 24362438.

A. Rubel 1986 Axisymmetric shear flow over spheres and spheroids. AIAA J. 24, 630634.

B. Turkington 1989 Vortex rings with swirl: axisymmetric solutions of the Euler equations with nonzero helicity. SIAM J. Math Anal. 20, 5773.

J.-Z. Wu , H.-Y. Ma & M.-D. Zhou 2006 Vorticity and Vortex Dynamics. Springer.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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