Viscously controlled nonlinear magnetoconvection in a non-uniformly stratified horizontal fluid layer

Abstract

Weakly nonlinear analysis is adopted in order to study a model of magnetoconvection in a rotating horizontal fluid layer. The layer is supposed to be non-uniformly stratified and is permeated by an azimuthal magnetic field. The only nonlinearity brought in this convecting system is due to presence of Ekman layers along the horizontal mechanical boundaries. The governing equations for this model together with the expression for geostrophic flow, i.e., modified Taylor's constraint are analysed with help of perturbation methods. As a result, the bifurcation structure in the vicinity of the critical Rayleigh number is revealed.