An Overview of the Flow Regimes in a Circular Couette System

  • C. D. Andereck
  • G. W. Baxter
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 41)


The flow of a fluid between concentric rotating cylinders constitutes one of the simplest situations for studying the formation of nonequilibrium structures, both static and time-dependent, that one could imagine. In spite of this simplicity it exhibits an amazingly rich range of possible states, only some of which are well understood. In this contribution we will give a brief review of some recent experimental observations, and note some of the areas in which theoretical insight exists and where it is lacking.


Secondary Flow Vortex Pair Outer Cylinder Large Vortex Boundary Wave 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H.A. Snyder: Int. J. Non-Lin. Mech. 5, 659 (1970).CrossRefGoogle Scholar
  2. 2.
    D. Coles: J. Fluid Mech. 21, 385 (1965).CrossRefzbMATHADSGoogle Scholar
  3. 3.
    P.S. Marcus: J. Fluid Mech. 146, 45 (1984).CrossRefzbMATHADSGoogle Scholar
  4. 4.
    P.S. Marcus: J. Fluid Mech. 146, 65 (1984).CrossRefzbMATHADSGoogle Scholar
  5. 5.
    R.C. DiPrima, H.L. Swinney: In Hydrodynamic Instabilities and the Transition to Turbulence, 2nd edition, ed. by H.L. Swinney and J.P. Gollub, Springer Series in Applied Physics, Vol. 45 (Springer, Berlin, Heidelberg, New York, 1985), p. 139.Google Scholar
  6. 6.
    G. Cognet, M. Douaya: Abstract from “Fifth Taylor-Vortex Flow Working Party”, Tempe, Arizona (1987).Google Scholar
  7. 7.
    J.E. Burkhalter, E.L. Koschmieder: J. Fluid Mech. 58, 547 (1973).CrossRefADSGoogle Scholar
  8. 8.
    H.A. Snyder: unpublished preprint (1969).Google Scholar
  9. 9.
    P. Matisse, M. Gorman: Phys. Fluids 27, 759 (1984).CrossRefADSGoogle Scholar
  10. 10.
    M.A. Dominguez-Lerma, G. Ahlers, D.S. Cannell: Phys. Fluids 28, 1204 (1985).CrossRefADSGoogle Scholar
  11. 11.
    C.D. Andereck, R. Dickman, H.L. Swinney: Phys. Fluids 26, 1395 (1983).CrossRefADSGoogle Scholar
  12. 12.
    C.D. Andereck, S.S. Liu, H.L. Swinney: J. Fluid. Mech. 164, 155 (1986).CrossRefADSGoogle Scholar
  13. 13.
    G.W. Baxter, C.D. Andereck: Phys. Rev. Lett. 57, 3046 (1986).CrossRefADSGoogle Scholar
  14. 14.
    G.P. King, H.L. Swinney: Phys. Rev. A27, 1240 (1983).ADSGoogle Scholar
  15. 15.
    M.A. Gorman, H.L. Swinney: J. Fluid Mech. 117, 123 (1982).CrossRefADSGoogle Scholar
  16. 16.
    R.S. Shaw, C.D. Andereck, L.A. Reith, H.L. Swinney: Phys. Rev. Lett. 48, 1172 (1982).CrossRefADSGoogle Scholar
  17. 17.
    A. Brandstater, J. Swift, H.L. Swinney, A. Wolf, J.D. Farmer, E. Jen, J.P. Crutchfield: Phys. Rev. Lett. 51, 1442 (1983).CrossRefADSMathSciNetGoogle Scholar
  18. 18.
    G.P. Smith, A.A. Townsend: J. Fluid Mech. 123, 187(1982).CrossRefADSGoogle Scholar
  19. 19.
    D. Rand: Arch. Rat. Mech. Anal. 79, 1 (1982).CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    M. Renardy: Arch. Rat. Mech. Anal. 79, 49 (1982).zbMATHMathSciNetGoogle Scholar
  21. 21.
    H.R. Brand: Prog. Theor. Phys. 71, 1096 (1984).CrossRefADSGoogle Scholar
  22. 22.
    H.R. Brand, M.C. Cross: Phys. Rev. A27, 1237 (1983).CrossRefADSGoogle Scholar
  23. 23.
    G. Ahlers, D.S. Cannell, M.A. Dominguez-Lerma: Phys. Rev. Lett. 48, 368 (1982).CrossRefADSGoogle Scholar
  24. 24.
    D.S. Cannell, M.A. Dominguez-Lerma, G. Ahlers: Phys. Rev. Lett. 50, 1365 (1983).CrossRefADSGoogle Scholar
  25. 25.
    C. VanAtta: J. Fluid Mech. 25, 495 (1966).CrossRefADSGoogle Scholar
  26. 26.
    E.R. Krueger, A. Gross, R.C. DiPrima: J. Fluid Mech. 24, 521 (1966).CrossRefADSGoogle Scholar
  27. 27.
    R.C. DiPrima, R.N. Grannick: In Instability of Continuous Systems, ed. by. H. Leipholz (Springer-Verlag, Berlin, Heidelberg, 1971), p. 55.CrossRefGoogle Scholar
  28. 28.
    Y. DeMay, G. Iooss: J. Mec. Theor. Appl., numero special, 193 (1984).Google Scholar
  29. 29.
    G. Iooss: this volume.Google Scholar
  30. 30.
    P. Chossat, G. Iooss: Japan J. Appl. Math. 2, 37 (1985).CrossRefzbMATHMathSciNetGoogle Scholar
  31. 31.
    P. Chossat, Y. Demay, G. Iooss: preprint (1986).Google Scholar
  32. 32.
    M. Golubitsky, I. Stewart: SIAM J. Math. Anal. 17, 249 (1986).CrossRefzbMATHADSMathSciNetGoogle Scholar
  33. 33.
    H.A. Snyder: Phys. Fluids 11, 728 (1968).CrossRefADSGoogle Scholar
  34. 34.
    H.A. Snyder: Phys. Fluids 11, 1599 (1968).CrossRefADSGoogle Scholar
  35. 35.
    R. Tagg: Abstract from “Fifth Taylor Vortex Working Party”, Tempe, Arizona (1987).Google Scholar
  36. 36.
    C. Stern, A.K.M.F. Hussain: Abstract from “Fifth Taylor Vortex Working Party”, Tempe, Arizona (1987).Google Scholar
  37. 37.
    R. Friedrich, Th. Grauer, H. Haken: Abstract from “Fifth Taylor Vortex Working Party”, Tempe, Arizona (1987).Google Scholar
  38. 38.
    R. Tagg: private communication.Google Scholar
  39. 39.
    H.R. Brand: Phys. Rev. A32, 3551 (1985).ADSGoogle Scholar
  40. 40.
    M. Nagata: J. Fluid Mech. 169 229 (1986).CrossRefzbMATHADSGoogle Scholar
  41. 41.
    G. Iooss: J. Fluid mech. 173, 273 (1986).CrossRefzbMATHADSGoogle Scholar
  42. 42.
    G.W. Baxter, J. Hegseth, C.D. Andereck: to be published.Google Scholar
  43. 43.
    J.D. Keeler, J.D. Farmer: In Spatio-Temporal Coherence and Chaos in Physical Systems, ed. by A.R. Bishop, G. Grüner, B. Nicolaenko (North-Holland, Amsterdam, Oxford, New York, 1986), p. 413.Google Scholar
  44. 44.
    M.A. Domiguez-Lerma, D.S. Cannell, G. Ahlers: Phys. Rev. A34 4956 (1986).ADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • C. D. Andereck
    • 1
  • G. W. Baxter
    • 1
    • 2
  1. 1.Department of PhysicsThe Ohio State UniversityColumbusUSA
  2. 2.Department of PhysicsDuke UniversityDurhamUSA

Personalised recommendations