  In confined rotating convection, a strong zonal flow can develop close to the
side wall with a modal structure that precesses anti-cyclonically (counter to
the applied rotation) along the side wall. It is surmised that this is a robust
non-linear evolution of the wall modes observed before the onset of bulk
convection. Here, we perform direct numerical simulations of cylindrically
confined rotating convection at high rotation rates and strong turbulent
forcing. Through comparison with earlier work, we find a fit-parameter-free
relation that links the angular drift frequency of the robust wall mode
observed far into the turbulent regime with the critical wall mode frequency at
onset, firmly substantiating the connection between the observed boundary zonal
flow and the wall modes. Deviations from this relation at stronger turbulent
forcing suggest early signs of the bulk turbulence starting to hamper the
development of the wall mode. Furthermore, by studying the interactive flow
between the robust wall mode and the bulk turbulence, we identify radial jets
penetrating from the wall mode into the bulk. These jets induce a large scale
multipolar vortex structure in the bulk turbulence, dependent on the wavenumber
of the wall mode. In a narrow cylinder the entire bulk flow is dominated by a
quadrupolar vortex driven by the radial jets, while in a wider cylinder the
jets are found to have a finite penetration length and the vortices do not
cover the entire bulk. We also identify the role of Reynolds stresses in the
generation of zonal flows in the region near the sidewall.
