Hostname: page-component-89b8bd64d-dvtzq Total loading time: 0 Render date: 2026-05-12T07:05:55.815Z Has data issue: false hasContentIssue false
  • English
  • Français

Determination of two-dimensional magnetostatic equilibria and analogous Euler flows

Published online by Cambridge University Press:  26 April 2006

D. Linardatos
D. Linardatos
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

The equivalence of the method of magnetic relaxation to a variational problem with an infinity of constraints is established. This variational problem is solved in principle and approximations to the exact solution are compared to results obtained by numerical relaxation of fields with a single stationary elliptic point. In the case of a finite energy field of the above topology extending to infinity, we show that the minimum energy state is the one in which all field lines are concentric circles and that this state is topologically accessible from the original one. This state is used as a reference state for understanding the relaxation of fields constrained by finite boundaries. We then consider the relaxation of fields containing saddle points and confirm the tendency of the saddle points to collapse and form two Y-points. An infinite family of local equilibrium solutions each describing a Y-point is provided.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 246 , January 1993 , pp. 569 - 591
Copyright
© 1993 Cambridge University Press

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.)

Article purchase

Temporarily unavailable

References

Arnol'd, V. I. 1974 The asymptotic Hopf invariant and its applications. In Proc. Summer School in Differential Equations. Erevan: Armenian SSR Academy of Science. (English transl. Sel. Math, Sov. 5, 1986, 327–345.)
Arrowsmith, D. K. & Place, C. M. 1990 An Introduction to Dynamical Systems. Cambridge University Press.
Bajer, K. 1989 Flow kinematics and magnetic equilibria. PhD thesis, Cambridge University.
Batchelor, G. K. 1955 On steady laminar flow with closed streamlines at large Reynolds number. J. Fluid Meck. 1, 177– 190.Google Scholar
Boyd, J. P. & Ma, H. 1990 Numerical study of elliptical modons using a spectral method. J. Fluid Mech. 221, 597– 611.Google Scholar
Freedman, M. H. 1988 A note on topology and magnetic energy in incompressible perfectly conducting fluids. J. Fluid Mech. 194, 549– 551.Google Scholar
Iserles, A. & Nørsett, S. P. 1991 Order Stars. Chapman & Hall.
Moffatt, H. K. 1985 Magnetostatic equilibria and analogous Euler flows of arbitrary complex topology. Part 1. Fundamentals. J. Fluid Much. 159, 359– 378.Google Scholar
Moffatt, H. K. 1986 On the existence of localized rotational disturbances which propagate without change of structure in an inviscid fluid. J. Fluid Mech. 173, 289– 302.Google Scholar
Moffatt, H. K. 1988 Generalised vortex rings with and without swirl. Fluid Dyn, Res. 3, 22– 30.Google Scholar
Moffatt, H. K. 1990 Structure and stability of solutions of the Euler equations: a lagrangian approach. Phil. Tran, R. Soc. Land. A 333, 321– 342.Google Scholar
Parker, E. N. 1983 Heating of the outer solar atmosphere. In Solar-Terrestrial Physics (ed. R. L. Carovillano & J. M. Forbes), pp. 129– 154, D. Reidel.
Parker, E. N. 1987 Magnetic reorientation and the spontaneous formation of tangential discontinuities in deformed magnetic fields, Astrophys, J. 318, 876– 887.Google Scholar
Parker, E. N. 1990 Spontaneous tangential discontinuities and the optical analogy for static magnetic fields VI. Topology of currents sheets. Geophys. Astrophys, Fluid Dyn. 53, 43– 80.Google Scholar
Vainshtein, S. I. 1990 Cusp-points and current sheet dynamics. Astron. Astrophys. 230, 238– 243.Google Scholar