High Rayleigh number thermal convection in volumetrically heated spherical shells

摘要

We conducted experiments of isoviscous thermal convection in homogeneous, volumetrically heated spherical shells with various combinations of curvature, rate of internal heating, and Rayleigh number. We define a characteristic temperature adapted to volumetrically heated shells, for which the appropriate Rayleigh number, measuring the vigor of convection, is RaVH = (1 + f + f ~2)/ 3αρ ~2gHD ~5 /ηkκ, where f is the ratio between the inner and outer radii of the shell. Our experiments show that the scenario proposed by Parmentier and Sotin (2000) to describe convection in volumetrically heated 3D-Cartesian boxes fully applies in spherical geometry, regardless of the shell curvature. The dynamics of the thermal boundary layer are controlled by both newly generated instabilities and surviving cold plumes initiated by previous instabilities. The characteristic time for the growth of instabilities in the thermal boundary layer scales as RaVH ~(-1/2), regardless of the shell curvature. We derive parameterizations for the average temperature of the shell and for the temperature jump across the thermal boundary layer, and find that these quantities are again independent of the shell curvature and vary as RaVH ~(-0.238) and RaVH ~(-1/4), respectively. These findings appear to be valid down to relatively low values of the Rayleigh-Roberts number, around 10 ~5.