Weakly Nonlinear Analysis of Rotating Anisotropic Ferromagnetic Rayleigh-Bénard convection

The instabilities occurring in a horizontal layer of ferromagnetic fluid which is heated from below and kept rotating about vertical axis in the presence of vertical magnetic fluid is analysed using weakly nonlinear analysis. It is observed that either stationary convection or oscillatory convection occurred as the first instability depending on the control parameters. The amplitude equations are derived in the vicinity of the onset of stationary convection and oscillatory convection by assuming the fluid as anisotropic. At the onset of stationary convection the conditions for generalized Eckhuas instability and near the Liptz point the conditions for zig zag instability are obtained. Localized convection is studied from cubic-quintic amplitude equation. Heat transfer rate in terms of the Nusselt number is computed from the cubic amplitude equation. From the cubic-quintic amplitude equation, the subcritical fluid behavior near the onset of oscillatory convection is analysed.