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We demonstrate a reduction in the measured inner wall shear stress in moderately turbulent Taylor-Couette flows by depositing sprayable superhydrophobic microstructures on the inner rotor surface. The magnitude of reduction becomes progressively larger as the Reynolds number increases up to a value of 22% at Re=8. 010^4. We show that the mean skin friction coefficient C₅ in the presence of the superhydrophobic coating can be fitted to a modified Prandtl--von K\'arm\'an--type relationship of the form (C₅/2) ^-1/2=Mln (Re (C₅/2) ^1/2) +N+ (b/) Re (C₅/2) ^1/2 from which we extract an effective slip length of b19. The dimensionless effective slip length b^+=b/_, where _ is the viscous length scale, is the key parameter that governs the drag reduction and is shown to scale as b^+Re^1/2 in the limit of high Re.
Srinivasan et al. (Tue,) studied this question.