  The precise mechanism that forms jets and large-scale vortices on the giant
planets is unknown. An inverse cascade has been suggested. Alternatively,
energy may be directly injected by small-scale convection. Our aim is to
clarify whether an inverse cascade feeds zonal jets and large-scale eddies in a
system of rapidly rotating, deep, geostrophic spherical-shell convection. We
analyze the nonlinear scale-to-scale transfer of kinetic energy in such
simulations as a function of the azimuthal wave number, m. We find that the
main driving of the jets is associated with upscale transfer directly from the
small convective scales to the jets. This transfer is very nonlocal in spectral
space, bypassing large-scale structures. The jet formation is thus not driven
by an inverse cascade. Instead, it is due to a direct driving by Reynolds
stresses from small-scale convective flows. Initial correlations are caused by
the effect of uniform background rotation and shell geometry on the flows.
While the jet growth suppresses convection, it increases the correlation of the
convective flows, which further amplifies the jet growth until it is balanced
by viscous dissipation. To a much smaller extent, energy is transferred upscale
to large-scale vortices directly from the convective scales, mostly outside the
tangent cylinder. There, large-scale vortices are not driven by an inverse
cascade either. Inside the tangent cylinder, the transfer to large-scale
vortices is weaker, but more local in spectral space, leaving open the
possibility of an inverse cascade as a driver of large-scale vortices. In
addition, large-scale vortices receive kinetic energy from the jets via forward
transfer. We therefore suggest a jet instability as an alternative formation
mechanism of largescale vortices. Finally, we find that the jet kinetic energy
scales as $\ell^{-5}$, the same as for the zonostrophic regime.
