Effects of curvature, aspect ratio and plan form in two- and three-dimensional spherical models of thermal convection

Abstract

Abstract Three-dimensional models of thermal convection in a spherical shell are presented for five different cases, each characterized by a unique ratio, f, of the radii of the inner and outer bounding surfaces. These solutions are compared to comparable two-dimensional solutions in axisymmetric spherical, cylindrical and Cartesian coordinates. All solutions were obtained with a Rayleigh number of 105, stress free, isothermal boundaries and no internal heating in a constant property Boussinesq fluid of infinite Prandtl number. Similarities and differences between three-dimensional and two-dimensional curvilinear models are discussed in terms of scales and stability of the flow patterns, mean radial 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-dimensional curvilinear models, provided the aspect ratio and plan form of the flow solutions are comparable. The mean temperature is found to be sensitive to curvature and plan form but not to aspect ratio, while the Nusselt number is found to be sensitive to curvature and aspect ratio but not to the plan form of the flow.