  We study rapidly-rotating Boussinesq convection driven by internal heating in
a full sphere. We use a numerical model based on the quasi-geostrophic
approximation for the velocity field, whereas the temperature field is
three-dimensional. This approximation allows us to perform simulations for
Ekman numbers down to 1e-8, Prandtl numbers relevant for liquid metals (~0.1)
and Reynolds numbers up to 3e4. Persistent zonal flows composed of multiple
jets form as a result of the mixing of potential vorticity. For the largest
Rayleigh numbers computed, the zonal velocity is larger than the convective
velocity despite the presence of boundary friction. The convective structures
and the zonal jets widen when the thermal forcing increases. Prograde and
retrograde zonal jets are dynamically different: in the prograde jets (which
correspond to weak potential vorticity gradients) the convection transports
heat efficiently and the mean temperature tends to be homogenised; by contrast,
in the cores of the retrograde jets (which correspond to steep gradients of
potential vorticity) the dynamics is dominated by the propagation of Rossby
waves, resulting in the formation of steep mean temperature gradients and the
dominance of conduction in the heat transfer process. Consequently, in
quasi-geostrophic systems, the width of the retrograde zonal jets controls the
efficiency of the heat transfer.
