Nonlinear magneto-convection due tocompositional and thermal buoyancy withSoret effect

Abstract

The linear stability of magnetoconvection due to compositional and ther-mal buoyancy has been investigated. We have obtained the values of Takens-Bogdanovbifurcation points by plotting graphs of neutral curves corresponding to stationary and os-cillatory convection for different values of physical parameters relevant to magnetoconvec-tion in Earth’s outer core. We have derived a nonlinear two-dimensional Landau-Ginzburgequation with real coefficients near the onset of stationary convection at a supercriticalpitchfork bifurcation and two nonlinear two-dimensional coupled Landau-Ginzburg typeequations with complex coefficients near the onset of oscillatory convection at a supercrit-ical Hopf bifurcation. We have discussed the stability regions of standing and travellingwaves. We have also discussed the occurence of secondary instabilities such as Eckhaus,zigzag and Benjamin-Feir instabilities