Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-19T10:20:34.801Z Has data issue: false hasContentIssue false
  • English
  • Français

Axisymmetric Couette flow at large Taylor numbers

Published online by Cambridge University Press:  20 April 2006

A. A. Townsend
A. A. Townsend
Affiliation:
Emmanuel College, Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

Measurements have been made in flow between concentric cylinders with only the inner one rotating, for Reynolds numbers (based on flow gap) from 17 000 to 120 000, corresponding to Taylor numbers from 8 × 107 to 4 × 109. At the lower speeds (Reynolds numbers less than 30 000), the large-scale motion consists of toroidal eddies, highly uniform in spacing and intensity and convected by a slow axial flow past fixed sensors. By synchronizing an external oscillator with the passage frequency, flow velocity and small-scale turbulent intensity may be sampled at defined stages of the passage cycle and averaged to provide maps of the velocity fields and the associated distributions of small-scale intensity and Reynolds stress.

At higher speeds, the passage of toroidal eddies becomes too irregular to establish the passage cycle, but, by comparing the velocity fluctuations from four inclined hot wires placed near the outer cylinder, the current location of large-scale flow separation from the outer cylinder can be approximately determined. Statistics of the temporal variations of the location show that the large-scale motion still approximates to the toroidal form, but that there are azimuthal variations of separation position and velocity that indicate a change from toroidal to helical eddies. Conditional averages of flow velocity and small-scale turbulent intensity, based on relative distance from the position of flow separation, are very similar in form and magnitude to phase-selected averages obtained at lower speeds.

The considerable changes in the large-scale motion that occur as the Reynolds number increases from 300 to 1200 times the critical value are believed to arise from increase in the ‘turbulent Taylor number’ of the central flow, based on variation of angular momentum and on the eddy diffusion coefficients for linear and angular momentum. Effects on the motion of the slow axial flow, always less than 1% of the peripheral flow velocity, are also discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 144 , July 1984 , pp. 329 - 362
Copyright
© 1984 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barcilon, A., Brindley, J., Lessen, M. & Mobbs, F. R. 1979 J. Fluid Mech. 94, 453.
Bouabdallah, A. & Cognet, G. 1980 In Laminar-Turbulent Transition (ed. R. Eppler & H. Fasel), p. 368. Springer.
Coles, D. 1965 J. Fluid Mech. 21, 385.
Davey, A., Di Prima, R. C. & Stuart, J. T. 1968 J. Fluid Mech. 31, 17.
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.
Koschmieder, E. L. 1979 J. Fluid Mech. 93, 515.
Smith, G. P. & Townsend, A. A. 1982 J. Fluid Mech. 123, 187.
Smith, G. P. & Townsend, A. A. 1983 In Structure of Complex Turbulent Flows (ed. R. Dumas & L. Fulachier), p. 185. Springer.
Zaman, K. B. M. Q. & Husain, A. K. M. F. 1980 J. Fluid Mech. 101, 449.