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Instability of magnetic modons and analogous Euler flows

Published online by Cambridge University Press:  13 March 2009

A. Y. K. Chui  and
H. K. Moffatt
A. Y. K. Chui
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW, UK
H. K. Moffatt
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW, UK
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Abstract

We construct numerical examples of a ‘modon’ (counter-rotating vortices) in an Euler flow by exploiting the analogy between steady Euler flows and magnetostatic equilibria in a perfectly conducting fluid. A numerical modon solution can be found by determining its corresponding magnetostatic equilibrium, which we refer to as a ‘magnetic moclon’. Such an equilibrium is obtained numerically by a relaxation procedure that conserves the topology of the relaxing field. Our numerical results show how the shape of a magnetic modon depends on its ‘signature’ (magnetic flux profile), and that these magnetic modons are unexpectedly unstable to non-symmetric perturbations. Diffusion can change the topology of the field through a reconnection process and separate the two magnetic eddies. We further show that the analogous Euler flow (or modon) behaves similar to a perturbed Hill's vortex.

Type
Research Article
Information
Journal of Plasma Physics , Volume 56 , Issue 3: Special Issue: Honour of David Montgomery , December 1996 , pp. 677 - 691
Copyright
Copyright © Cambridge University Press 1996

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References

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