van den Berg Thomas H, Doering Charles R, Lohse Detlef, Lathrop Daniel P
Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Sep;68(3 Pt 2):036307. doi: 10.1103/PhysRevE.68.036307. Epub 2003 Sep 12.
We examine the torque required to drive the smooth or rough cylinders in turbulent Taylor-Couette flow. With rough inner and outer walls the scaling of the dimensionless torque G is found to be consistent with pure Kolmogorov scaling G approximately Re2. The results are interpreted within the Grossmann-Lohse theory for the relative role of the energy dissipation rates in the boundary layers and in the bulk; as the boundary layers are destroyed through the wall roughness, the torque scaling is due only to the bulk contribution. For the case of one rough and one smooth wall, we find that the smooth cylinder dominates the dissipation rate scaling, i.e., there are corrections to Kolmogorov scaling. A simple model based on an analogy to electrical circuits is advanced as a phenomenological organization of the observed relative drag functional forms. This model leads to a qualitative prediction for the mean velocity profile within the bulk of the flow.
