  Motivated by understanding the dynamics of stellar and planetary interiors,
we have performed a set of direct numerical simulations of Boussinesq
convection in a rotating full sphere. The domain is internally heated with
fixed temperature and stress-free boundary conditions, but fixed heat flux and
no-slip boundary conditions are also briefly considered. We particularly focus
on the large-scale coherent structures and the mean zonal flows that can
develop in the system. At Prandtl number of unity, as the thermal forcing
(measured by the Rayleigh number) is increased above the value for the onset of
convection, we find a relaxation oscillation regime, followed by a geostrophic
turbulence regime. Beyond this we see for the first time the existence of
large-scale coherent vortices that form on the rotation axis. All regime
boundaries are well described by critical values of the convective Rossby
number $Ro_c$, with transitions from oscillatory to geostrophic turbulence, and
then to the large-scale vortex regime at values $Ro_c\approx 0.2$ and
$Ro_c\approx 1.5$, respectively. The zonal flow is controlled by the convective
Rossby number and changes its direction when the flow transitions from the
geostrophic turbulence regime to the large-scale vortex regime. While the
non-zonal flow speed and heat transfer can be described by the so-called
inertial scaling in the geostrophic turbulence regime, the formation of
large-scale vortices appears to reduce both the non-zonal flow speed and the
efficiency of convective heat transfer.
