  We characterize the two-dimensionalization process in the turbulent flow
produced by an impeller rotating at a rate $\omega$ in a fluid rotating at a
rate $\Omega$ around the same axis for Rossby number $Ro=\omega/\Omega$ down to
$10^{-2}$. The flow can be described as the superposition of a large-scale
vertically invariant global rotation and small-scale shear layers detached from
the impeller blades. As $Ro$ decreases, the large-scale flow is subjected to
azimuthal modulations. In this regime, the shear layers can be described in
terms of wakes of inertial waves traveling with the blades, originating from
the velocity difference between the non-axisymmetric large-scale flow and the
blade rotation. The wakes are well defined and stable at low Rossby number, but
they become disordered at $Ro$ of order of 1. This experiment provides insight
into the route towards pure two-dimensionalization induced by a background
rotation for flows driven by a non-axisymmetric rotating forcing.
