Journal of Fluid Mechanics

Papers

Steady axisymmetric vortex flows with swirl and shear

ALAN R. ELCRATa1, BENGT FORNBERGa2 and KENNETH G. MILLERa1

a1 Department of Mathematics, Wichita State University, Wichita, KS 67260, USA

a2 Department of Applied Mathematics, University of Colorado, Boulder, CO 80309, USA

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.

(Received December 28 2007)

(Revised July 02 2008)

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