  Since Taylor's seminal paper, the existence of large-scale quasi-axisymmetric
structures has been a matter of interest when studying Taylor-Couette flow. In
this manuscript, we probe their formation in the highly turbulent regime by
conducting a series of numerical simulations at a fixed Reynolds number
$Re_s=3.6\times 10^4$ while varying the Coriolis parameter to analyze the flow
characteristics as the structures arise and dissipate. We show how the Coriolis
force induces a one-way coupling between the radial and azimuthal velocity
fields inside the boundary layer, but in the bulk there is a two-way coupling
that causes competing effects. We discuss how this complicates the analogy of
narrow-gap Taylor-Couette to other convective flows. We then compare these
statistics to a similar shear flow without no-slip boundary layers, showing how
this double coupling causes very different effects. We finish by reflecting on
the possible origins of turbulent Taylor rolls.
