Large scale instabilities in two-dimensional magnetohydrodynamics

Details Large scale instabilities in two-dimensional magnetohydrodynamics Large scale instabilities in two-dimensional magnetohydrodynamics

1998-10-21

arxiv.org/abs/chao-dyn/9810026v1

Nonlinear Sciences

Chaotic Dynamics

6 pages RevTeX, 6 PostScript figures

Scientific paper

The stability of a sheared magnetic field is analyzed in two-dimensional magnetohydrodynamics with resistive and viscous dissipation. Using a multiple-scale analysis, it is shown that at large enough Reynolds numbers the basic state describing a motionless fluid and a layered magnetic field, becomes unstable with respect to large scale perturbations. The exact expressions for eddy-viscosity and eddy-resistivity are derived in the nearby of the critical point where the instability sets in. In this marginally unstable case the nonlinear phase of perturbation growth obeys to a Cahn-Hilliard-like dynamics characterized by coalescence of magnetic islands leading to a final new equilibrium state. High resolution numerical simulations confirm quantitatively the predictions of multiscale analysis.

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