  Wall-roughness induces extra drag in wall-bounded turbulent flows. Mapping
any given roughness geometry to its fluid dynamic behaviour has been hampered
by the lack of accurate and direct measurements of skin-friction drag. Here the
Taylor-Couette (TC) system provides an opportunity as it is a closed system and
allows to directly and reliably measure the skin-friction. However, the
wall-curvature potentially complicates the connection between the wall friction
and the wall roughness characteristics. Here we investigate the effects of a
hydrodynamically fully rough surface on highly turbulent, inner cylinder
rotating, TC flow. We find that the effects of a hydrodynamically fully rough
surface on TC turbulence, where the roughness height k is three orders of
magnitude smaller than the Obukhov curvature length Lc (which characterizes the
effects of curvature on the turbulent flow, see Berghout et al. arXiv:
2003.03294, 2020), are similar to those effects of a fully rough surface on a
flat plate turbulent boundary layer (BL). Hence, the value of the equivalent
sand grain height ks, that characterizes the drag properties of a rough
surface, is similar to those found for comparable sandpaper surfaces in a flat
plate BL. Next, we obtain the dependence of the torque (skin-friction drag) on
the Reynolds number for given wall roughness, characterized by ks, and find
agreement with the experimental results within 5 percent. Our findings
demonstrate that global torque measurements in the TC facility are well suited
to reliably deduce wall drag properties for any rough surface.
