Effects of thermal boundary condition on convection in rapidly rotating spherical shells

Two-dimensional thermal convection in a rotating cylindrical annulus under a fixed heat flux boundary condition is examined in order to consider the effects of thermal boundary condition on convection in rapidly rotating spherical shells. Nonlinear numerical calculations show the existence of a state where convection cells with a small horizontal scale are superimposed in cells with a large horizontal scale in the case of a constant coefficient of topographic β effect. However, when the effect of a spherical boundary is included, small scale cells in a large clockwise circulation disappear and they exists only in a large anti-clockwise circulation. Such asymmetric emergence of small scale cells is consistent with the expectation by Orr mechanism. The linear stability analyses of a three-dimensional system of rotating spherical shells also suggest the emergence of convection cells with a large horizontal scale under the fixed heat flux condition.