Nonlinear Convection in Earth's Outer Core

I worked on linear and weakly non-linear theories on magneto convection in a rotating fluid with isotropic/anisotropic diffusivities using analytical methods. In linear stability analysis, we have determined the marginal stability curves at the onset of stationary and oscillatory convection using one-term Galerkin method. In weakly nonlinear analysis, a two dimensional non-linear amplitude equation near the onset of stationary and oscillatory convection has been derived. Conditions for the occurrence of secondary instabilities such as Eckhaus and Zigzag instabilities are studied. Also, stability regions of travelling waves and standing waves are studied.