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Surface-layer similarity in turbulent circular Couette flow

Published online by Cambridge University Press:  20 April 2006

Martin Claussen
Martin Claussen
Affiliation:
Max-Planck-Institut für Meteorologie, Bundestrasse 55, 2000 Hamburg 13, F.R.G.
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Abstract

Smith & Townsend's (1982) experimental data on circular Couette flow are re-examined in the framework of surface-layer similarity theory. Surface-layer similarity of horizontally stratified shear flow is shown to have its counterpart in a narrow-gap Couette flow between concentric cylinders. Smith & Townsend's data of mean angular momentum and mean-velocity profiles in a region near a cylinder lend support to the applicability of Monin–Obukhov similarity to circular Couette flow. Only for flows of very high Reynolds numbers is a region of logarithmic variation of mean profiles found close to the cylinder wall. Because of curvature effects on the flow, the mean profiles deviate from the logarithmic profile as distance from the cylinder wall increases. For flows of sufficiently low Reynolds number, but still very high Taylor number, no logarithmic profile seems to exist; instead, profiles in the viscous region and in the outer region are connected to each other by a ‘free-convection (rotation)’ profile. From Smith & Townsend's data the velocity field is not observed to follow the prediction of ‘free-convection’ similarity; however, the ‘free-convection’ profile is found in the distribution of mean angular momentum.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 144 , July 1984 , pp. 123 - 131
Copyright
© 1984 Cambridge University Press

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References

Businger, J. A. 1973 A note on free convection. Boundary-Layer Met. 4, 323.Google Scholar
Dyer, A. J. & Bradley, E. F. 1982 An alternative analysis of flux-gradient relationships at the 1976 ITCE. Boundary-Layer Met. 22, 3.Google Scholar
Malkus, W. V. R. 1979 Turbulent velocity profiles from stability criteria. J. Fluid Mech. 90, 401.Google Scholar
Monin, A. S. & Obukhov, A. M. 1954 Fundamental Gesetzmäßigkeiten der turbulenter Vermischung in der bodennahen Schicht der Atmosphäre. Akad. Nauk. SSSR, Geofis. Inst. Trudy 151, 163. [Transl. in Sammelband zur statistischen Theorie der Turbulenz (ed. H. Goering). Berlin, 1958.]Google Scholar
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics, vol. I. MIT Press.
Obukhov, A. M. 1946 Turbulence in an atmosphere with a nonuniform temperature. Trudy Inst. Teoret. Geofis. Akad. Nauk SSSR. No. 1. [English Transl. in Boundary-Layer Met. 2 (1971), 7.]Google Scholar
Smith, G. P. & Townsend, A. A. 1982 Turbulent Couette flow between concentric cylinders at large Taylor numbers. J. Fluid Mech. 123, 187.Google Scholar
Taylor, G. I. 1936 Fluid friction between rotating cylinders. I. Torque measurements. Proc. R. Soc. Lond. A 157, 546.Google Scholar
Townsend, A. A. 1959 Temperature fluctuation over a heated horizontal surface. J. Fluid Mech. 5, 209.Google Scholar
Wang, A. K. M. & Gelhaar, I. W. 1970 Turbulent flow between concentric rotating cylinders. Ralph M. Parsons Lab. for Water Resources and Hydrodynamics, MIT, Rep. 132.Google Scholar