Effect of thermal stratification on the symmetry-breaking in a differentially-rotating spherical fluid shell

We consider the shear flow between double concentric spherical boundaries. Under the effect of rotation of the inner boundary (spherical Couette flow), the axisymmetric/non-axisymmetric transition from the trivial state is determined by the radius ratio β of the inner to outer spheres, which has been confirmed experimentally by Nakabayashi(2002) and Egbers(1995). With the comparison to previous studies, we have developed a direct numerical scheme to realize the spherical Couette flow under the weak effect of thermal stratification between the spherical boundaries, which has been unexplored. Here, restricting our attention to the case of non-axisymmetric transition (the radius ratio β>0.3), we numerically investigated the effect on the symmetry-breaking of the shear flow by the weak thermal stratification. In the non-rotating case, under the thermal effect a variety of states are bifurcated from the trivial conductive state at a critical Grashof number. We found that, at a relatively larger rotation number, the thermal effect reduces the transition Grashof number at which the (trivial) axisymmetric state bifurcates into a non-axisymmetric state. Our numerical results predict that axisymmetric states are realized only at less than a certain finite Grashof number.