Stability of time-periodic flows in a Taylor-Couette geometry

  • Christiane Normand
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 549)


The flows generated by the time-periodic forcing of one or both cylinders of the Taylor-Couette system are of two types: either modulated or pulsed flows whether or not there exists a mean rotation. Their linear stability is analysed within the frame of Floquet theory which predicts synchronous or subharmonic instability modes, a phenomenon known as parametric resonance. The non linear dynamics of time-periodic Taylor vortex flow has been examined both by numerical simulations and through model equations. We shall report on the results of two analytical approaches. The first one due to Hall [18] is based on an amplitude equation which was then modified by Barenghi and Jones [5] to account for imperfections in the system. The second one is a Lorenz model derived by Kuhlmann et al. [22].


Outer Cylinder Amplitude Equation Floquet Theory Taylor Number Taylor Vortex 
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  1. 1.
    G. Ahlers, P. Hohenberg, M. Lücke: Phys. Rev A 32, 3493 (1985)CrossRefADSGoogle Scholar
  2. 2.
    A. Aouidef, C. Normand, A. Stegner and J. E. Wesfreid: Phys. Fluids 11, 3665 (1994)CrossRefADSGoogle Scholar
  3. 3.
    A. Aouidef and C. Normand: C. R. Acad. Sci. Paris, Serie II b, 322, 545 (1996)zbMATHGoogle Scholar
  4. 4.
    A. Aouidef and C. Normand: to be published in Eur. J. Mech. B/FluidsGoogle Scholar
  5. 5.
    C. F. Barenghi and C. A. Jones: J. Fluid Mech. 208, 127 (1989)zbMATHCrossRefADSMathSciNetGoogle Scholar
  6. 6.
    J. K. Battacharjee, K. Banerjee and K. Kumar: J. Phys. A L19, 835(1986)ADSGoogle Scholar
  7. 7.
    R. J. Braun, G. B. McFadden, B. T. Murray, S. R. Coriell, M. E. Glicksman, M. E. Selleck: Phys. Fluids A 5, 1891 (1993)zbMATHCrossRefADSGoogle Scholar
  8. 8.
    S. Carmi and J. I. Tustaniwskyj: J. Fluid Mech. 108, 19 (1981)zbMATHCrossRefADSGoogle Scholar
  9. 9.
    S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford University Press, London, 1961).zbMATHGoogle Scholar
  10. 10.
    S. H. Davis: Ann. Rev. Fluid Mech. 8, 57 (1976)CrossRefADSGoogle Scholar
  11. 11.
    R. J. Donnelly: Proc. Roy. Soc. London A 281, 130 (1964)ADSCrossRefGoogle Scholar
  12. 12.
    P. G. Drazin and W. H. Reid: Hydrodynamics Stability (Cambridge University Press, 1981)Google Scholar
  13. 13.
    P. Ern: Instabilités d’écoulements périodiques en temps avec effets de courbure et de rotation, Thése de doctorat, Université Paris VI (1997)Google Scholar
  14. 14.
    P. Ern and J. E. Wesfreid: J. Fluid Mech. 397, 73 (1999).zbMATHCrossRefADSGoogle Scholar
  15. 15.
    M. Faraday: Phil. Trans. R. Soc. London 52, 319 (1831)Google Scholar
  16. 16.
    G. Z. Gershuni, E. M. Zhukhovitskii: Convective Stability of Incompressible Fluids (Keter Publishing House, Jerusalem 1976)Google Scholar
  17. 17.
    P. Hall: Proc. Roy. Soc. London A 344, 453 (1975)zbMATHADSCrossRefGoogle Scholar
  18. 18.
    P. Hall: J. Fluid Mech. 67, 29 (1975)zbMATHCrossRefADSGoogle Scholar
  19. 19.
    P. Hall: Proc. Roy. Soc. London A 359, 151 (1978)zbMATHADSCrossRefGoogle Scholar
  20. 20.
    P. Hall: J. Fluid Mech. 126, 357 (1983)zbMATHCrossRefADSGoogle Scholar
  21. 21.
    H. Kuhlmann: Phys. Rev. A 32, 1703 (1985)CrossRefADSGoogle Scholar
  22. 22.
    H. Kuhlmann, D. Roth, M. Lücke: Phys. Rev. A 39, 745(1989)CrossRefADSGoogle Scholar
  23. 23.
    E. N. Lorenz, J. Atmos. Sci. 20, 130 (1963)CrossRefADSGoogle Scholar
  24. 24.
    B. T. Murray, G. B. McFadden and S. R. Coriell: Phys. Fluids A2, 2147 (1990)Google Scholar
  25. 25.
    P. J. Riley and R. L. Laurence: J. Fluid Mech. 75, 625(1976)zbMATHCrossRefADSGoogle Scholar
  26. 26.
    G. Seminara, P. Hall: Proc. R. Soc. London A 350, 299 (1976)zbMATHADSCrossRefGoogle Scholar
  27. 27.
    G. I. Taylor: Philos. Trans. R. Soc. London A 223, 289 (1923)CrossRefADSGoogle Scholar
  28. 28.
    S. G. K. Tennakoon, C. D. Andereck, A. Aouidef, C. Normand: Eur. J. Mech. B/Fluids 16, 227 (1997)zbMATHGoogle Scholar
  29. 29.
    J. I. Tustaniwskyj and S. Carmi: Phys. Fluids 23, 1732 (1980)zbMATHCrossRefADSGoogle Scholar
  30. 30.
    R. Thompson: Instabilities of some time-dependent flows. Ph.D. Thesis, Massachussetts Institute of Technology (1968)Google Scholar
  31. 31.
    C. von Kerczek and S. H. Davis: J. Fluid Mech. 62, 753 (1974)zbMATHCrossRefADSGoogle Scholar
  32. 32.
    T. J. Walsh, R. J. Donnelly: Phys. Rev. Lett. 58, 2543 (1988)CrossRefADSGoogle Scholar
  33. 33.
    T. J. Walsh, R. J. Donnelly: Phys. Rev. Lett. 60, 700 (1988)CrossRefADSGoogle Scholar
  34. 34.
    X. Wu, J. B. Swift: Phys. Rev. A 40, 7197 (1989)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Christiane Normand
    • 1
  1. 1.C.E.A/SaclayService de Physique ThéoriqueGif-sur-Yvette CedexFrance

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