Nonlinear Magneto Convection in a Rotating Fluid due to Vertical Magnetic Field and Vertical Axis of Rotation

In the present paper, linear and weakly nonlinear analysis of magnetoconvection in a rotating fluid due to the vertical magnetic field and the vertical axis of rotation are presented. For linear stability analysis, the normal mode analysis is utilized to find the Rayleigh number which is the function of Taylor number, Magnetic Prandtl number, Thermal Prandtl number and Chandrasekhar number. Also, the correlation between the Rayleigh number and wave number is graphically analyzed. The parameter regimes for the existence of pitchfork, Takens-Bogdanov and Hopf bifurcations are reported. Small-amplitude modulation is considered to derive the Newell-Whitehead-Segel equation and using its phase-winding solution, the conditions for the occurrence of Eckhaus and zigzag secondary instabilities are obtained. The system of coupled Landau-Ginzburg equations is derived. The travelling wave and standing wave solutions for the Newell-Whitehead-Segel equation are also presented. For, standing waves and travelling waves, the stability regions are identified.