Hostname: page-component-77c89778f8-swr86 Total loading time: 0 Render date: 2024-07-21T00:41:06.309Z Has data issue: false hasContentIssue false
  • English
  • Français

On flow between counter-rotating cylinders

Published online by Cambridge University Press:  20 April 2006

C. A. Jones
C. A. Jones
Affiliation:
School of Mathematics, University of Newcastle upon Tyne, U.K.
Get access Rights & Permissions [Opens in a new window]

Abstract

Axisymmetric flows between counter-rotating cylinders of varying radius ratio are examined. The stability of these flows to non-axisymmetric disturbances is considered, and the results of these calculations are compared with experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 120 , July 1982 , pp. 433 - 450
Copyright
© 1982 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

Benjamin, T. B. & Mullin, T. 1981 Anomalous modes in the Taylor experiment. Proc. R. Soc. Lond. A 337, 221–249.Google Scholar
Booz, O. 1980 Numerische Lösung der Navier-Stokes-Gleichangen für Taylor-Wirbelströmungen im weiten Spalt. Ph.D. thesis, Stuttgart University.
Chandrasekhar, S. 1958 The stability of viscous flow between rotating cylinders. Proc. R. Soc. Lond. A 246, 301–311.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic stability. Clarendon.
Clenshaw, C. W. 1955 A note on the summation of Chebyshev series. Math. Tables & Aids to Computation 9, 118–120.Google Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385–425.Google Scholar
Davey, A., DiPrima, R. C. & Stuart, J. T. 1968 On the instability of Taylor vortices. J. Fluid Mech. 31, 17–52.Google Scholar
Diprima, R. C. & Eagles, P. M. 1977 An empirical torque relation for supercritical flow between rotating cylinders. Phys. Fluids 20, 171–175.Google Scholar
Diprima, R. C. & Grannick, R. N. 1971 A nonlinear investigation of the stability of flow between counter-rotating cylinders. In Proc. IUTAM Symp. 1969, Instability of Continuous Systems (ed. H. Leipholz), pp. 51–60. Springer.
Donnelly, R. J. & Fultz, D. 1960 Experiments on the stability of viscous flow between rotating cylinders. II. Visual Observations. Proc. R. Soc. Lond. A 258, 101–123.Google Scholar
Donnelly, R. J. & Schwarz, K. W. 1965 Experiments on the stability of viscous flow between rotating cylinders. Proc. R. Soc. Lond. A 283, 531–546.Google Scholar
Hildebrand, F. B. 1956 Introduction to Numerical Analysis. McGraw-Hill.
Jones, C. A. 1981 Nonlinear Taylor vortices and their stability. J. Fluid Mech. 102, 253–265.Google Scholar
Kirchgassner, K. & Sorger, P. 1969 Branching analysis for the Taylor problem. Quart. J. Mech. Appl. Math. 22, 183–209.Google Scholar
Krueger, E. R., Gross, A. & DiPrima, R. C. 1966 On the relative importance of Taylorvortex and non-axisymmetric modes in flow between rotating cylinders. J. Fluid Mech. 24, 521–538.Google Scholar
Moore, D. R. & Weiss, N. O. 1973 Nonlinear penetrative convection. J. Fluid Mech. 61, 553–581.Google Scholar
Musman, S. 1968 Penetrative convection. J. Fluid Mech. 31, 343–360.Google Scholar
Nakaya, C. 1975 The second stability boundary for circular Couette flow. J. Phys. Soc. Japan 38, 576–585.Google Scholar
Nissan, A. H., Nardacci, J. L. & Ho, C. Y. 1963 The onset of different modes of instability for flow between rotating cylinders. A.I.Ch.E. J. 9, 620–624.Google Scholar
Snyder, H. A. 1968 Stability of rotating Couette flow. I. Asymmetric waveforms. Phys. Fluids 11, 728–734.Google Scholar
Snyder, H. A. 1969a Wavenumber selection at finite amplitude in rotating Couette flow. J. Fluid Mech. 35, 273–299.Google Scholar
Snyder, H. A. 1969b Change in waveform and mean flow associated with wavelength variations in rotating Couette flow. J. Fluid Mech. 35, 337–353.Google Scholar
Veronis, G. 1963 Penetrative convection. Astrophys. J. 137, 641–663.Google Scholar