Prandtl number effects on the stability of natural convection between spherical shells

An analysis of the effect of the Prandtl number on the linear stability of axisymmetric (m = 0) disturbances on steady natural convection contained between two concentric spherical shells when the gap is narrow are presented. The disturbance equations are solved using a truncated spectral series. Convergence of the series is examined. Prandtl numbers range from 0 to 100 while the relative gap-width is either 0.100, 0.075, or 0.050. Results confirm the hypothesis that experimentally observed changes in the basic motion for certain flow parameters are due to its instability and indicate that for any Prandtl number larger than a transition value, the unstable flows evolve to a steady pattern while for smaller Prandtl numbers the bifurcated flows are time periodic.