Abstract: We investigate properties of convective solutions of the
Boussinesq thermal convection in a moderately rotating spherical
shell allowing the inner and outer sphere rotation due to the viscous
torque of the fluid. The ratio of the inner and outer radii of the
spheres, the Prandtl number and the Taylor number are fixed to 0.4,
1 and 5002, respectively. The inertial moments of the inner and outer
spheres are fixed to about 0.22 and 100, respectively. The Rayleigh
number is varied from 2.6 × 104 to 3.4 × 104. In this parameter
range, convective solutions transit from equatorially symmetric quasiperiodic
ones to equatorially asymmetric chaotic ones as the Rayleigh
number is increased. The transition route in the system allowing
rotation of both the spheres is different from that in the co-rotating
system, which means the inner and outer spheres rotate with the
same constant angular velocity: the convective solutions transit as
equatorially symmetric quasi-periodic solution → equatorially symmetric
chaotic solution → equatorially asymmetric chaotic solution
in the system allowing both the spheres rotation, while equatorially
symmetric quasi-periodic solution → equatorially asymmetric quasiperiodic
solution → equatorially asymmetric chaotic solution in the
co-rotating system.