EFFECTS OF CURVATURE, ASPECT RATIO AND PLAN FORM IN 2-DIMENSIONAL AND3-DIMENSIONAL SPHERICAL-MODELS OF THERMAL-CONVECTION

Three-dimensional models of thermal convection in a spherical shell ar e presented for five different cases, each characterized by a unique r atio, f, of the radii of the inner and outer bounding surfaces. These solutions are compared to comparable two-dimensional solutions in axis ymmetric spherical, cylindrical and Cartesian coordinates. All solutio ns were obtained with a Rayleigh number of 10(5), stress free, isother mal boundaries and no internal heating in a constant property Boussine sq fluid of infinite Prandtl number. Similarities and differences betw een three-dimensional and two-dimensional curvilinear models are discu ssed in terms of scales and stability of the flow patterns, mean radia l temperature profiles and heat transport. It is shown that diagnostic statistics such as mean temperature and Nusselt number may be scaled from one degree of curvature to another for both three- and two-dimens ional curvilinear models, provided the aspect ratio and plan form of t he flow solutions are comparable. The mean temperature is found to be sensitive to curvature and plan form but not to aspect ratio, while th e Nusselt number is found to be sensitive to curvature and aspect rati o but not to the plan form of the flow.