Nonlinear magneto-convection due to compositional and thermal buoyancy with Soret effect

Abstract

The linear stability of magnetoconvection due to compositional and thermal buoyancy has been investigated. We have obtained the values of Takens-Bogdanov bifurcation points by plotting graphs of neutral curves corresponding to stationary and oscillatory convection for different values of physical parameters relevant to magnetoconvection in Earth's outer core. We have derived a nonlinear two-dimensional Landau-Ginzburg equation with real coefficients near the onset of stationary convection at a supercritical pitchfork bifurcation and two nonlinear two-dimensional coupled Landau-Ginzburg type equations with complex coefficients near the onset of oscillatory convection at a supercritical Hopf bifurcation. We have discussed the stability regions of standing and traveling waves. We have also discussed the occurence of secondary instabilities such as Eckhaus, zigzag and Benjamin-Feir instabilities.