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Wall-roughness induces extra drag in wall-bounded turbulent flows. Mappingany given roughness geometry to its fluid dynamic behaviour has been hamperedby the lack of accurate and direct measurements of skin-friction drag. Here theTaylor-Couette (TC) system provides an opportunity as it is a closed system andallows to directly and reliably measure the skin-friction. However, thewall-curvature potentially complicates the connection between the wall frictionand the wall roughness characteristics. Here we investigate the effects of ahydrodynamically fully rough surface on highly turbulent, inner cylinderrotating, TC flow. We find that the effects of a hydrodynamically fully roughsurface on TC turbulence, where the roughness height k is three orders ofmagnitude smaller than the Obukhov curvature length Lc (which characterizes theeffects 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 aflat plate turbulent boundary layer (BL). Hence, the value of the equivalentsand grain height ks, that characterizes the drag properties of a roughsurface, is similar to those found for comparable sandpaper surfaces in a flatplate BL. Next, we obtain the dependence of the torque (skin-friction drag) onthe Reynolds number for given wall roughness, characterized by ks, and findagreement with the experimental results within 5 percent. Our findingsdemonstrate that global torque measurements in the TC facility are well suitedto reliably deduce wall drag properties for any rough surface.

Characterizing the turbulent drag properties of rough surfaces with a Taylor--Couette setup