Convection in Earth's Outer Core due to Thermal Compositional Buoyancy

Nonlinear convection due to Thermal and Compositional buoyancy in Earth's outer core has been investigated. We have obtained the values of Takens-Bogdanov bifurcation points and codimension-two bifurcation points by plotting graphs of neutral curves corresponding to stationary and oscillatory convection for different values of physical parameters. We have studied Nusselt number from Landau-Ginzburg equation at the onset of stationary convection for the steady case. We have also derived a nonlinear two dimensional Landau-Ginzburg equation near the onset of stationary convection at a supercritical pitchfork bifurcation and nonlinear one-dimensional coupled Landau-Gingburg type equations near the onset of oscillatory convection at a supercritical Hopf bifurcation. We have discussed the stability regions of standing and travelling waves. We have also discussed the occurrence of secondary instabilities such as Eckhaus, Zigzag and Benjamin-Feir instabilities.