Thermal blob convection in spherical shells

We present experimental and numerical results on convection of high Prandtl number fluids in a spherical shell of aspect ratio image, with the inner sphere cooled and the outer sphere heated. For sufficiently small Rayleigh numbers the flow is both axisymmetric and steady, consisting of fluid streaming off the south pole of the inner sphere, and returning in the equatorial regions. For larger Ra this streaming flow becomes time-dependent, with thermal blobs periodically dripping off the south pole. For even greater Ra these pulses become irregular in time. An axisymmetric numerical code is then used to study this phenomenon in more detail. The numerical results agree qualitatively (but not quantitatively) with the experimental results, and suggest furthermore that the transition from regular to irregular behavior may occur via a period-doubling cascade. The numerical code is used to explore the Pr and β dependence of this dripping blob phenomenon, and reveals the results to be independent of Prandtl number for image. In contrast, the aspect ratio plays an important role, with no distinct blobs observed if β is too small.