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Nelin. Dinam., 2015, Volume 11, Number 2, Pages 241–266 (Mi nd478)  

Original papers

Nonlinear dynamo theory

M. I. Koppab, A. V. Turc, V. V. Yanovskiiba

a Institute for Single Crystals of NAS of Ukraine Lenin Ave. 60, Kharkov, 61001, Ukraine
b V.N.Karazin Kharkov National University Svobody Sq. 4, Kharkov, 61022, Ukraine
c Université de Toulouse [UPS], CNRS, Institut de Recherche en Astrophysique et Planétologie 9 avenue du Colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France

Abstract: Using the asymptotic method of multiple scales construct nonlinear theory of large-scale structures in stratified conducting medium in the presence of small-scale oscillations of the velocity field and magnetic fields. Such small-scale stationary oscillations are generated by small external sources at low Reynolds numbers. The nonlinear system of equations describing the evolution of largescale structure of the velocity field and the magnetic fields are obtained. The linear stage of evolution leads to the well known instability. We study the equations of non-linear instability and its stationary solutions.

Keywords: stratified conducting medium, nonlinear system of equations, instability, large scale structures, multiscale method

Full text: PDF file (444 kB)
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UDC: 533.9, 532.5
MSC: 76E25, 76E30
Received: 30.12.2014
Revised: 16.02.2015

Citation: M. I. Kopp, A. V. Tur, V. V. Yanovskii, “Nonlinear dynamo theory”, Nelin. Dinam., 11:2 (2015), 241–266

Citation in format AMSBIB
\Bibitem{KopTouYan15}
\by M.~I.~Kopp, A.~V.~Tur, V.~V.~Yanovskii
\paper Nonlinear dynamo theory
\jour Nelin. Dinam.
\yr 2015
\vol 11
\issue 2
\pages 241--266
\mathnet{http://mi.mathnet.ru/nd478}


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  • Нелинейная динамика
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