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Unstable transition properties of the driven magnetohydrodynamic sheet pinch

Published online by Cambridge University Press:  21 April 2006

R. B. Dahlburg ,
T. A. Zang  and
D. Montgomery
R. B. Dahlburg
Affiliation:
Department of Physics, College of William and Mary, Williamsburg, VA 23185 Present address: Laboratory for Computational Physics, Naval Research Laboratory, Washington DC 20375.
T. A. Zang
Affiliation:
NASA Langley Research Center, Hampton, VA 23665
D. Montgomery
Affiliation:
Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755
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Abstract

The unstable transition behaviour of a bounded, current-carrying, two-dimensional magnetofluid is explored, using the hydrodynamic theory developed for parallel shear flows as a guide. The time development of a perturbed driven magnetohydrodynamic sheet pinch is simulated numerically. The nonlinear partial differential equations of two-dimensional, incompressible, viscoresistive magnetohydrodynamics are advanced in time numerically by means of a semi-implicit, mixed Fourier collocation-finite difference algorithm. Nonlinear excitation of the higher wavenumbers results in the development of electric current sheets of finite extent, as well as the formation of ‘attraction currents’ centred at the magnetic O-points. A secondary instability mechanism, the dynamic tearing of the electric current sheet, is also observed. This dynamic tearing leads to sawtooth-like temporal oscillations in certain global quantities. The long time state of the system resembles a nonlinearly saturated state with significant excitation of many wavenumbers. Some features of this state can be understood by means of a Landau nonlinear stability theory based on certain assumptions about the perturbation energy balance.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 169 , August 1986 , pp. 71 - 107
Copyright
© 1986 Cambridge University Press

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