A weakly nonlinear stability of centrally symmetric magnetohydrodynamic systems to perturbations involving large scales |
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| Authors: | V A Zheligovsky |
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| Institution: | (1) International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Moscow, Russia;(2) Laboratory of General Aerodynamics, Institute of Mechanics, Moscow State University, Michurinskii pr. 1, Moscow, 117192, Russia |
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| Abstract: | The problem of weakly nonlinear stability of 3-D centrally symmetric magnetohydrodynamic systems to perturbations involving large scales is considered. It is assumed that large space-time scales are absent in the magnetohydrodynamic state under study, which is stable with respect to perturbations whose scales are as small as those of the state itself. Equations derived by asymptotic methods for average fields of perturbations generalize the Navier-Stokes and magnetic induction equations. They include a combined eddy diffusion operator, generally anisotropic and not necessarily negative definite, and additional quadratic terms. An effective method is proposed for the calculation of coefficients of eddy diffusion and advection in equations governing average fields. |
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