Hostname: page-component-848d4c4894-2xdlg Total loading time: 0 Render date: 2024-06-22T11:10:37.406Z Has data issue: false hasContentIssue false
  • English
  • Français

Marginal instability in Taylor–Couette flows at a very high Taylor number

Published online by Cambridge University Press:  19 April 2006

A. Barcilon ,
J. Brindley ,
M. Lessen  and
F. R. Mobbs
A. Barcilon
Affiliation:
Geophysical Fluid Dynamics Institute, Florida State University
J. Brindley
Affiliation:
Department of Applied Mathematical Studies, University of Leeds
M. Lessen
Affiliation:
Department of Mechanical and Aerospace Sciences, University of Rochester
F. R. Mobbs
Affiliation:
Department of Mechanical Engineering, University of Leeds
Get access Rights & Permissions [Opens in a new window]

Abstract

We report on a set of turbulent flow experiments of the Taylor type in which the fluid is contained between a rotating inner circular cylinder and a fixed concentric outer cylinder, focusing our attention on very large Taylor number values, i.e. \[ 10^3 \leqslant T/T_c \leqslant 10^5, \] where Tc is the critical value of the Taylor number T for onset of Taylor vortices. At such large values of T, the turbulent vortex flow structure is similar to the one observed when T – Tc is small and this structure is apparently insensitive to further increases in T. These flows are characterized by two widely separated length scales: the scale of the gap width which characterizes the Taylor vortex flow and a much smaller scale which is made visible by streaks in the form of a ‘herring-bone’-like pattern visible at the walls. These are conjectured to be Görtler vortices which arise as a result of centrifugal instability in the wall boundary layers. Ideas of marginal instability by which we postulate that both the Taylor and Görtler vortex structures are marginally unstable on their own scale seem to provide good quantitative agreement between predicted and observed Görtler vortex spacings.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 94 , Issue 3 , 16 October 1979 , pp. 453 - 463
Copyright
© 1979 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. & Lessen, M. 1978 Tellus 30, 557–562.
Coles, D. 1965 J. Fluid Mech. 21, 385–425.
Gollub, J. P. & Swinney, H. L. 1975 Phys. Rev. Lett. 35, 927.
Görtler, H. 1940 Nachr. Ges. Wiss. Göttingen, Maths. Phys. Kl. 1, 1–26 (translated as N.A.C.A. Tech. Mem. no. 1375).
Hammerlin, G. 1956 Z. angew. Math. Phys. 7, 156–164.
Lessen, M. 1978 J. Fluid Mech. 88, 535–540.
Lessen, M., Barcilon, A. & Butler, T. E. 1977 J. Fluid Mech. 82, 449–454.
Lessen, M. & Singh, P. J. 1974 Phys. Fluids 17, 1329–1331.
Lessen, M. & Paillet, F. L. 1976 Phys. Fluids 19, 942–945.
Pai, S. I. 1943 N.A.C.A. Tech. Note no. 892.
Short, M. G. & Jackson, J. H. 1977 In Superlaminar Flow in Bearings, Proc. 2nd Leeds—Lyon Symp. Tribology (ed. D. Dowson, M. Godet and C. M. Taylor), pp. 28–33. Lond. Inst. of Mech. Eng.
Snyder, H. A. 1970 Int. J. Non-linear Mech. 5, 659–685.
Swinney, H. L., Fenstermacher, P. R. & Gollub, J. P. 1977 In Synergetics (ed. H. Haken), pp. 60–69. Springer.
Taylor G. I. 1923 Phil. Trans. Roy. Soc. A 223, 289–343.
Taylor, G. I. 1935 Proc. Roy. Soc. A 151, 494–512.
Wattendorf, F. L. 1935 Proc. Roy. Soc. A 148, 565–598.