Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-16T07:15:46.455Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Arakawa, A. 1966 Computational design for long-term numerical integration of the equations of fluid motion: two-dimensional incompressible flow. Part I. J. Comp. Phys. 1, 119–143.CrossRefGoogle Scholar
Boyd, J. P. and Ma, H. 1990 Numerical study of elliptical modons using a spectral method. J. Fluid Mech. 221, 597–611.CrossRefGoogle Scholar
Davidson, P. A. 1994 Global stability of two-dimensional and axisymmetric Euler flows. J. Fluid Mech. 276, 273–306.CrossRefGoogle Scholar
Eydeland, A. and Turkington, B. 1988 A computational method of solving free boundary problem in vortex dynamics. J. Comp. Phys. 78, 194–214.CrossRefGoogle Scholar
Linardatos, D. 1993 Determination of two-dimensional magnetostatic equilibria and analogous Euler flows. J. Fluid Mech. 246, 569–591.CrossRefGoogle Scholar
Moffatt, H. K. 1985 Magnetostatic equilibria and analogous Euler flows of arbitrary complex topology. Part I. Fundamentals. J. Fluid Mech. 159, 359–378.CrossRefGoogle Scholar
Moffatt, H. K. 1986 a On the existence of localized rotational disturbances which propagate without change of structure in an inviscid fluid. J. Fluid Mech. 173, 289–302.CrossRefGoogle Scholar
Moffatt, H. K. 1986 b Magnetostatic equilibria and analogous Euler flows of arbitrary complex topology. Part 2. Stability considerations. J. Fluid Mech. 166, 359–378.CrossRefGoogle Scholar
Moffatt, H. K. and Moore, D. W. 1978 The response of Hill's spherical vortex to a small axisymmetric disturbance. J. Fluid Mech. 87, 749–760.CrossRefGoogle Scholar
Pozrikidis, C. 1986 The nonlinear instability of Hill's vortex. J. Fluid Mech. 168, 337–367.CrossRefGoogle Scholar
Rosenbluth, M. N. and Bussac, M. N. 1979 MHD stability of spheromak. Nucl. Fusion 19, 489–498.CrossRefGoogle Scholar