Buoyancy-driven convective flows play a crucial role in geophysics and atmosphere for global heat and momentum transport. We present the main numerical results for the worldwide recognized GeoFlow experiment that is performed on the International Space Station (ISS) and AtmoFlow experiment that is in the preparation phase. In both cases, a radial force field is produced due to the dielectrophoretic effect .The Coriolis and centrifugal forces are taken into account as well. While in the GeoFlow experiment the inner and outer surfaces are maintained at constant temperatures, a laterally dependent thermal boundary conditions are used in the AtmoFlow. It is necessary because the solar radiation is responsible for the differential heating of the Earths surface: the temperature has a maximin value at the equator and becomes colder in the vicinity of the poles. The influence of the internal heating is taken into account in the energy equation. The new thermal boundary conditions lead to the unexpected dynamical features of the supercritical flows. Critical Rayleigh number increases with increasing in Taylor number in the GeoFlow case according to Rac~Ta^0.7 law if the internal heating is negligible and linear if the internal heating becomes important. But in the AtmoFlow case the stability diagram has a closed shape, i.e. the range, in which the flow is stable to infinitesimal perturbations, bounded by the intervals (0, Ta), (0, Ra_{Ec}) and the stability curve. The specific computer code based on very exact spectral methods has been developed to enable such investigations in the spherical geometry.