Simulation details. All simulations are run at $Pr=1$ and $\eta=0.6$. The columns from left to right indicate: case number, Rayleigh number $Ra$, Rossby number $Ro$, the number of grid points in the longitudinal, radial, and co-latitudinal direction $N_\theta \times N_r \times N_\varphi$. A rotational symmetry order $n_s$ is applied to reduce computational costs, indicating the longitude of the computational domain as $2\pi/n_s$. The average heat transfer $Nu$ across the inner and the outer sphere, and the regional heat transfer across the outer sphere $Nu_{I,II,III}$ (see figure 3(b) of the manuscript). Note that region $\mathrm{II}$ and $\mathrm{III}$ are only defined when a maximum prograde velocity is identified.