Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-28T06:21:49.454Z Has data issue: false hasContentIssue false
  • English
  • Français

Notes on the multiplicity of flows in the Taylor experiment

Published online by Cambridge University Press:  20 April 2006

T. Brooke Benjamin  and
T. Mullin
T. Brooke Benjamin
Affiliation:
Mathematical Institute, 24/29 St Giles, Oxford OX1 3LB, U.K.
T. Mullin
Affiliation:
Mathematical Institute, 24/29 St Giles, Oxford OX1 3LB, U.K.
Get access Rights & Permissions [Opens in a new window]

Abstract

A representative set of experimental observations is presented demonstrating a remarkably large number of distinct steady flows that all subsist on the same boundary conditions. Commentary on the significance of these and related findings re-emphasizes previous proposals about the interpretation of the Taylor experiment.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 121 , August 1982 , pp. 219 - 230
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

Alziary De Roquefort, T. & Grillaud, G. 1978 Computations of Taylor vortex flow by a transient implicit method. Comp. Fluids 6, 259–269.Google Scholar
Benjamin, T. B. 1976 Applications of Leray–Schauder degree theory to problems of hydrodynamic stability. Math. Proc. Comb. Phil. Soc. 79, 373–392.Google Scholar
Benjamin, T. B. 1978a Bifurcation phenomena in steady flows of a viscous liquid. I. Theory. Proc. R. Soc. Lond. A 359, 1–26.Google Scholar
Benjamin, T. B. 1978b Bifurcation phenomena in steady flows of a viscous liquid. II. Experiments. Proc. R. Soc. Lond. A 359, 27–43.Google Scholar
Benjamin, T. B. 1978c Applications of generic bifurcation theory in fluid mechanics. In Contemporary Developments in Continuum Mechanics and Partial Differential Equations (ed. G. M. de la Penha & L. A. Medeiros). North-Holland.
Benjamin, T. B. 1981 New observations in the Taylor experiment. In Transition and Turbulence (ed. R. E. Meyer), pp. 25–41. Maths Res. Center, Univ. of Wisconsin, Symp. Series. Academic.
Benjamin, T. B. & Mullin, T. 1981 Anomalous modes in the Taylor experiment. Proc. R. Soc. Lond. A 377, 221–249.Google Scholar
Burkhalter, J. E. & Koschmieder, E. L. 1974 Steady supercritical Taylor vortices after sudden starts. Phys. Fluids 17, 1929–1935.Google Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385–425.Google Scholar
Diprima, R. C. & Swinney, H. L. 1981 Instabilities and transition in the flow between concentric rotating cylinders. In Hydrodynamic Instabilities and the Transition to Turbulence (ed. H. L. Swinney & J. P. Gollub), pp. 139–180. Springer.
Gorman, N. & Swinney, H. L. 1982 Spatial and temporal characteristics of modulated waves in the circular Couette system. J. Fluid Mech. 117, 123–142.Google Scholar
Kogelman, S. & DiPrima, R. C. 1970 Stability of spatially periodic supercritical flows in hydrodynamics. Phys. Fluids 13, 1–11.Google Scholar
Kusnetsov, E. A., Lvov, V. S., Nesterikhin, Y. E., Shmojlov, Y. F., Sobolev, V. S., Spector, M. D., Timokhin, S. A., Utkin, E. N. & Vasilenko, Y. G. 1977 About turbulence arising in Couette flow. Inst. Automation and Electrometry, Siberian Branch, U.S.S.R. Acad. Sci., Preprint no. 58.
Mullin, T. 1982 Mutations of steady cellular flows in the Taylor experiment. J. Fluid Mech. 121, 207–218.Google Scholar
Mullin, T. & Benjamin, T. B. 1980 Transition to oscillatory motion in the Taylor experiment. Nature 288, 567–569.Google Scholar
Mullin, T., Benjamin, T. B., Schätzel, K. & Pike, E. R. 1981 New aspects of unsteady Couette flow. Phys. Lett. 83 A, 333–336.Google Scholar
Mullin, T., Pfister, G. & Lorenzen, A. 1982 New observations on hysteresis effects in Taylor–Couette flow. Phys. Fluids. (to appear).
Nakaya, C. 1974 Domain of stable periodic vortex flows in a viscous fluid between concentric circular cylinders. J. Phys. Soc. Japan 36, 1164–1173.Google Scholar
Pfister, G. & Rehberg, I. 1981 Space-dependent order parameter in circular Couette flow. Phys. Lett. 83 A, 19–22.Google Scholar
Stuart, J. T. & DiPrima, R. C. 1978 The Eckhaus and Benjamin–Feir resonance mechanisms. Proc. R. Soc. Lond. A 362, 27–41.Google Scholar