Weakly nonlinear stability of magnetohydrodynamic systems with a center of symmetry to perturbations, involving large scales

Details Weakly nonlinear stability of magnetohydrodynamic systems with a center of symmetry to perturbations, involving large scales Weakly nonlinear stability of magnetohydrodynamic systems with a center of symmetry to perturbations, involving large scales

2006-01-05

arxiv.org/abs/nlin/0601012v1

Physics of the Earth (3), 2006, 69-78 (English translation: Izvestiya, Physics of the Solid Earth 42 (3), 2006, 244-253)

Nonlinear Sciences

Chaotic Dynamics

Latex, 15 pp. Accepted in Physics of the Earth, 2006 (in Russian). (English translation: Izvestiya, Physics of the Solid Earth

Scientific paper

I consider the problem of weakly nonlinear stability of three-dimensional parity-invariant magnetohydrodynamic systems to perturbations, involving large scales. I assume that the MHD state, the stability of which I investigate, does not involve large spatio-temporal scales, and it is stable to perturbations involving the same small spatial scales, as the perturbed MHD state. Mean-field equations, which I derive for the perturbation using asymptotic techniques for multiscale systems, are a generalization of the standard equations of magnetohydrodynamics (the Navier-Stokes equation with the Lorentz force and the magnetic induction equation). In them, the operator of combined eddy diffusivity emerges, which is in general anisotropic and not necessarily negatively defined, and new quadratic terms, analogous to the ones describing advection. A method for efficient computation of coefficients of the eddy diffusivity tensor and eddy advection terms in the mean-field equations is proposed.

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