Geometrical effects of curvature in axisymmetric spherical models of mantle convection

A two‐dimensional axisymmetric model of convection in a spherical shell has been developed in order to investigate the effects of curvature on model predictions of heat flow and temperature in the Earth's mantle. We restrict the solution domain to a belt centered midway between the poles of the axisymmetric coordinate system. This facilitates direct comparisons with models in cylindrical shells and plane layers, and avoids the physically unrealistic near‐pole effects associated with the axial symmetry at the poles. A boundary layer argument is suggested which accounts for the observed variations in heat flow and mean temperature from one level of curvature to another. In particular, plane layer results may be scaled to any desired degree of curvature. Similarities between previous model results in cylindrical shells and our results in spherical shells are noted, and it is shown that results in one geometry may be mapped into the other provided the ratio of the surface areas of the upper and lower boundaries is the same.