Weakly nonlinear stability of convective magnetohydrodynamic systems without alpha-effect to perturbations involving large scales

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dc.creatorZheligovsky, V.
dc.date2006-01-05
dc.date2006-09-25
dc.date.accessioned2026-07-07T10:14:19Z
dc.date.available2026-07-07T10:14:19Z
dc.descriptionI consider the problem of weakly nonlinear stability of three-dimensional convective magnetohydrodynamic systems, where there is no alpha-effect or it is insignificant, to perturbations involving large scales. I assume that the convective MHD state (steady or evolutionary), 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 state. Mean-field equations, which I derive for the perturbation using asymptotic techniques for multiscale systems, are a generalization of the equations of magnetohydrodynamics (the Navier-Stokes and magnetic induction equations). The operator of combined eddy diffusivity emerges, which is in general anisotropic and not necessarily negatively defined, as well as new quadratic terms analogous to the ones describing advection.
dc.descriptionLatex, 29 pp. Accepted in Physics of the Earth, 2006 (in Russian). (English translation: Izvestiya, Physics of the Solid Earth); typos corrected, minor changes in the text
dc.identifierhttps://arxiv.org/abs/nlin/0601013
dc.identifierhttp://arxiv.org/abs/nlin/0601013
dc.identifierPhysics of the Earth, 2006 (12), 92-108 (Engl. transl. Izvestiya, Physics of the Solid Earth, 42 (12), 2006, 1051-1068)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172839
dc.subjectChaotic Dynamics
dc.subjectFluid Dynamics
dc.titleWeakly nonlinear stability of convective magnetohydrodynamic systems without alpha-effect to perturbations involving large scales
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