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2003 A monotone iteration for axisymmetric vortices with swirl
Alan R. Elcrat, Kenneth G. Miller
Differential Integral Equations 16(8): 949-968 (2003).


We consider steady, inviscid axisymmetric vortex flows with swirl in a bounded channel, possibly with obstacles. Such flows can be obtained by solving the nonlinear equation \begin{equation} -\frac{\partial ^2\psi }{\partial z^2}-r\frac \partial {\partial r}(\frac 1r\frac{\partial \psi }{\partial r})=r^2f(\psi )+h(\psi ), \tag*{(0.1)} \end{equation} where $f$ and $h$ are given functions of the stream function $\psi$, with $\psi$ prescribed on the boundary of the flow domain. We use an iterative procedure to prove the existence of solutions to this Dirichlet problem under certain conditions on $f$ and $h$. Solutions are not unique, and relations between different families of solutions are obtained. These families include not only vortex rings with swirl, but also flows with tubular regions of swirling vorticity as occur in models of vortex breakdown.


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Alan R. Elcrat. Kenneth G. Miller. "A monotone iteration for axisymmetric vortices with swirl." Differential Integral Equations 16 (8) 949 - 968, 2003.


Published: 2003
First available in Project Euclid: 21 December 2012

zbMATH: 1161.76446
MathSciNet: MR1988954

Primary: 76B47
Secondary: 35Q35

Rights: Copyright © 2003 Khayyam Publishing, Inc.


Vol.16 • No. 8 • 2003
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