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On linear stability of steady space-periodic magnetohydrodynamic systems to perturbations involving large periods · arXivDesk

nlin/0512076Dec 30, 200516 pp., 1 Figure. In Russian

On linear stability of steady space-periodic magnetohydrodynamic systems to perturbations involving large periods

V. Zheligovsky

Chaotic Dynamics Fluid Dynamics

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Abstract

I construct a complete asymptotic expansion of solutions to the problem of linear stability of three-dimensional steady space-periodic magnetohydrodynamic states to perturbations involving large periods. Eddy diffusivity tensor is derived for parity-invariant steady states. I present numerical evidences that if perturbations of the flow are permitted, then the effect of negative eddy diffusivity emerges at much larger magnetic molecular diffusivities than in the kinematic dynamo problem (where no perturbations of the flow are assumed).

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The paper addresses: On linear stability of steady space-periodic magnetohydrodynamic systems to perturbations involving large periods.
I construct a complete asymptotic expansion of solutions to the problem of linear stability of three-dimensional steady space-periodic magnetohydrodynamic states to perturbations involving large periods.