  In this study, we combine experiments and direct numerical simulations to
investigate the effects of the height of transverse ribs at the walls on both
global and local flow properties in turbulent Taylor-Couette flow. We create
rib roughness by attaching up to 6 axial obstacles to the surfaces of the
cylinders over an extensive range of rib heights, up to blockages of 25% of the
gap width. In the asymptotic ultimate regime, where the transport is
independent of viscosity, we emperically find that the prefactor of the
$Nu_{\omega} \propto Ta^{1/2}$ scaling (corresponding to the drag coefficient
$C_f(Re)$ being constant) scales with the number of ribs $N_r$ and by the rib
height $h^{1.71}$. The physical mechanism behind this is that the dominant
contribution to the torque originates from the pressure forces acting on the
rib which scale with rib height. The measured scaling relation of $N_r
h^{1.71}$ is slightly smaller than the expected $N_r h^2$ scaling, presumably
because the ribs cannot be regarded as completely isolated but interact. In the
counter-rotating regime with smooth walls, the momentum transport is increased
by turbulent Taylor vortices. We find that also in the presence of transverse
ribs these vortices persist. In the counter-rotating regime, even for large
roughness heights, the momentum transport is enhanced by these vortices.
