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Turbulent Couette flow between concentric cylinders at large Taylor numbers

Published online by Cambridge University Press:  20 April 2006

G. P. Smith  and
A. A. Townsend
G. P. Smith
Affiliation:
Trinity Hall, Cambridge
A. A. Townsend
Affiliation:
Emmanuel College, Cambridge
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Abstract

Measurements have been made of the Couette flow in the annular space between concentric cylinders with a radius ratio of 1.5, the outer cylinder being held stationary and the inner one rotated at speeds to give Taylor numbers in the range 1.0 × 104−2.3 × l06 times the critical value for first instability of the steady viscous flow. Mean velocities have been measured both with Pitot tubes and with linearized hot-wire anemometers, and turbulent intensities and stresses, frequency spectra and space-time correlations have been obtained using single hot-wire anemometers of X-form and linear arrays of eight single-wire anemometers. For Taylor-number ratios to the critical number less than 3 × l05, the most prominent feature of the flow is a system of toroidal eddies, encircling the inner cylinder and uniformly spaced in the axial direction with nearly the separation of the Taylor vortices of the viscous instability. They are superimposed on a background of irregular motion and, except within the thin wall layers, the toroidal eddies contribute more to the total intensity. With increase of rotation speed, the toroidal eddies lose their regularity, and they cannot be clearly distinguished at Taylor-number ratios beyond 5 × l05.

The change of flow type from quasi-regular toroidal to fully irregular turbulent takes place over an extensive range of Taylor-number ratio centred near 3 × l05, and it may be linked with changes in the thin wall layers that separate the flow boundaries from the central region of nearly constant circulation. For ratios over 5 × l05, an appreciable part of the wall layers is comparatively unaffected by flow curvature and has a logarithmic distribution of mean velocity similar to that found in channel flows. It is suggested that the motion in the wall layers changes from a set of Gortler vortices characteristic of curved-wall flow to the more irregular motion found on plane walls, causing the toroidal eddies to break into sections of length ranging from a considerable fraction of the flow perimeter to nearly the separation of the cylinders. Changes in the frequency spectra of the radial and azimuthal velocit'y fluctuations are consistent with such a change.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 123 , October 1982 , pp. 187 - 217
Copyright
© 1982 Cambridge University Press

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References

Barcilon, A., Brindley, J., Lessen, M. & Mobbs, F. R. 1979 J. Fluid Mech. 94, 453.
Coles, D. 1965 J. Fluid Mech. 21, 385.
Di Prima, R. C. & Swinney, H. L. 1981 In Hydrodynamic Instabilities and the Transition to Turbulence (ed. H. L. Swinney & J. P. Gollub), p. 139. Springer.
Gollub, J. P. & Swinney, H. L. 1975 Phys. Rev. Lett. 35, 927.
Howard, L. N. 1963 J. Fluid Mech. 17, 405.
Koschmieder, E. L. 1979 J. Fluid Mech. 93, 515.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.
Malkus, W. V. R. 1954 Proc. R. Soc. Lond. A 225, 185.
Malkus, W. V. R. 1956 J. Fluid Mech. 1, 521.
Nakamura, I., Yamashita, S., Watanabe, T. & Sawaki, Y. 1981 In Proc. 3rd Symp. on Turbulent Flows; University of California, Davis.
Nickerson, E. C. 1969 J. Fluid Mech. 38, 807.
Roberts, P. H. 1965 Proc. R. Soc. Lond. A 283, 550.
Taylor, G. I. 1923 Phil. Trans. R. Soc. Lond. A 223, 289.
Taylor, G. I. 1936 Proc. R. Soc. Lond. A 158, 565.
Van Atta, C. 1966 J. Fluid Mech. 25, 495.
Wang, A. K. M. & Gelhar, L. W. 1970 M.I.T. Dept Civil Engng Rep. no. 132.