Rotating Rayleigh Bernard Convection with Variable Diffusive Coefficient

Abstract

The problem of rotating natural convective flow about the vertical axis, with variable viscosity confined between the two horizontal plates, is investigated via linear stability analysis. The transformed governing equations are solved numerically by using the Galerkin method. The computed results are compared for special cases with the results of earlier research by Chandrasekhar and Stengel et al., and are found to be in good agreement. We studied both stationary convection and oscillatory convection. The threshold values of Rayleigh number and wavenumber are computed and presented for various boundary conditions viz. rigid-rigid, rigid-free, free-rigid and free-free, and for different values of physical parameters viz. Taylor number Ta, viscosity ratio c and Prandtl number Pr. For rigid-rigid boundary conditions we studied the effect of c, Ta and Pr on the vertical velocity and temperature eigenfunctions at the onset. It is observed that the rotation rate stabilizes the dynamical system. The occurrence of the co-dimension two bifurcation point (CTP) is shown for various boundary conditions