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Nonlinear stationary magnetoconvection in a rotating fluid

Published online by Cambridge University Press:  01 October 1997

S. G. TAGARE
S. G. TAGARE
Affiliation:
Permanent address: School of Mathematics and Computer/Information Sciences, University of Hyderabad, Hyderabad 500 046, India. Inter-University Centre for Astronomy and Astrophysics, Ganeshkhind, Pune 411 007, India
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Abstract

We investigate finite-amplitude magnetoconvection in a rotating fluid in the presence of a vertical magnetic field when the axis of rotation is parallel to a vertical magnetic field. We derive a nonlinear, time-dependent, one-dimensional Landau–Ginzburg equation near the onset of stationary convection at supercritical pitchfork bifurcation when

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and a nonlinear time-dependent second-order ordinary differential equation when Ta=T*a (from below). Ta=T*a corresponds to codimension-two bifurcation (or secondary bifurcation), where the threshold for stationary convection at the pitchfork bifurcation coincides with the threshold for oscillatory convection at the Hopf bifurcation. We obtain steady-state solutions of the one-dimensional Landau–Ginzburg equation, and discuss the solution of the nonlinear time-dependent second-order ordinary differential equation.

Type
Research Article
Information
Journal of Plasma Physics , Volume 58 , Issue 3 , October 1997 , pp. 395 - 408
Copyright
1997 Cambridge University Press

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