Low-dimensional dynamics of axisymmetric modes in wavy Taylor vortex flow

  • Jan Abshagen
  • Gerd Pfister
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 549)


The dynamics of the ‘very-low-frequency’ (VLF) mode in moderate aspect ratio flow is experimentally investigated. The VLF mode is an axisymmetric, timedependent mode that occurs in wavy Taylor vortex flow at η = 0.5[25]. For normalised aspect ratios Γ/N < 0.89 a ‘universal’ sequence of states from stationary Taylor vortex flow to chaotic VLF mode has recently been discovered for the 10- to 50-vortex flow [26]. We show that a qualitatively different transition to chaos occurs in the 12-vortex flow compared with flow states having 14 and more vortices. A symmetry-breaking bifurcation that appears within this ‘universal’ sequence of states is found to be crucial for this new scenario. The onset of chaos via an intermittency route is accompanied with the restoring of the original Z 2-symmetry of the system leading to a ‘symmetric’ chaotic attractor for a wide range of aspect ratio. The formation of Shil'nikov-type attractor associated with the unstable symmetric fixed point could be found as well. Further investigations show that a new type of VLF mode appears in the Small-jet regime via a Hopf-bifurcation for slightly larger aspect ratio. We present additionally an examination of the VLF mode in a modulated wavy Taylor vortex flow consisting of Small-jet and axially localised Large-jet mode. The transition to chaos in these two VLF regimes is briefly discussed.


Chaotic Attractor Large Aspect Ratio Homoclinic Bifurcation Small Aspect Ratio Taylor Vortex 
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.
    M.C. Cross, P.C. Hohenberg: Rev.Mod.Phys. 65, 851 (1993)CrossRefADSGoogle Scholar
  2. 2.
    E.L. Koschmieder: Bénard Cells and Taylor Vortices, Cambridge UP (1993)Google Scholar
  3. 3.
    R. Tagg: Non.Sci.Today 4, 1 (1994)Google Scholar
  4. 4.
    J. Abshagen, A. Schulz, G. Pfister: in J. Parisi, S.C. Müller, W. Zimmermann (Eds.): Nonlinear Physics of Complex Systems, Lec.Notes Phys. 476, Springer (1996)Google Scholar
  5. 5.
    F.H. Busse, G. Pfister, D. Schwabe: in F.H. Busse, S.C. Müller (Eds.): Evolution of Spontaneous Structures in Dissipative Continuous Systems, Lec.Notes Phys., 55, Springer (1998)Google Scholar
  6. 6.
    T.B. Benjamin: Proc. R. Soc. (London) 359 (1978)Google Scholar
  7. 7.
    T. Mullin: J.Fluid Mech. 121, 207 (1982)CrossRefADSGoogle Scholar
  8. 8.
    J.P. Gollub, H.L. Swinney: Phys.Rev.Lett 35, 927 (1975)CrossRefADSGoogle Scholar
  9. 9.
    P.R. Fenstermacher, H.L. Swinney, J.P. Gollub: J.Fluid Mech. 94, 103 (1979)CrossRefADSGoogle Scholar
  10. 10.
    A. Brandstäter, J. Swift, H.L. Swinney, A. Wolf, J.D. Farmer, E. Jen, P.C. Crutchfield: Phys.Rev.Lett 51, 1442 (1983)CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    A. Brandstäter, H.L. Swinney: Phys.Rev A 35, 2207 (1987)CrossRefADSGoogle Scholar
  12. 12.
    G. Pfister, H. Schmidt, K.A. Cliffe, T. Mullin: J. Fluid Mech. 191, 1 (1988)CrossRefADSMathSciNetGoogle Scholar
  13. 13.
    G. Pfister: in G.E.A. Meier, F. Obermeier (Eds.): Flow of Real Fluids, Lec.Notes Phys. 235, Springer (1985)Google Scholar
  14. 14.
    Th. Buzug, J. von Stamm, G. Pfister: Phys.Rev.E 47, 1054 (1993)CrossRefADSGoogle Scholar
  15. 15.
    G. Pfister, A. Schulz, B. Lensch: Eur.J.Mech. B/Fluids 10, 247 (1991)Google Scholar
  16. 16.
    T. Mullin, K.A. Cliffe, G. Pfister: Phys.Rev.Lett. 58, 2212 (1987)CrossRefADSGoogle Scholar
  17. 17.
    T. Mullin, T.J. Price: Nature 54, 294 (1989)CrossRefADSGoogle Scholar
  18. 18.
    T.J. Price, T. Mullin: Physica D 48 (1991) 29–52zbMATHCrossRefADSMathSciNetGoogle Scholar
  19. 19.
    T. Mullin, J.J. Kobine: in P.T. Aston (Ed.): Nonlinear Mathematics and its applications, Cambridge UP (1996)Google Scholar
  20. 20.
    Th. Buzug, T. Reimers, G. Pfister: Europhys. Lett. 13, 605 (1990)CrossRefADSGoogle Scholar
  21. 21.
    Th. Buzug, G. Pfister: Phys.Rev.A 45, 7073 (1992)CrossRefADSGoogle Scholar
  22. 22.
    Th Buzug, G. Pfister: Physica D 58, 127 (1992)CrossRefADSGoogle Scholar
  23. 23.
    N. Enge, Th. Buzug, G. Pfister: Phys.Lett.A 175, 178 (1994)CrossRefADSMathSciNetGoogle Scholar
  24. 24.
    J. von Stamm, Th. Buzug, G. Pfister: Phys.Lett.A 194, 173 (1994)ADSCrossRefGoogle Scholar
  25. 25.
    U. Gerdts, J. von Stamm, Th. Buzug, G. Pfister: Phys.Rev.E 49, 4019 (1994)CrossRefADSGoogle Scholar
  26. 26.
    J. von Stamm, U. Gerdts, Th. Buzug, G. Pfister: Phys.Rev.E 54, 4938 (1996)CrossRefADSGoogle Scholar
  27. 27.
    J. Abshagen, G. Pfister: in preparationGoogle Scholar
  28. 28.
    A. Arneodo, P. Coullet, C. Tresser: J.Stat.Phys. 27, 171 (1982)zbMATHCrossRefMathSciNetADSGoogle Scholar
  29. 29.
    P. Glendinning, C. Sparrow: J.Stat.Phys. 35, 645(1984)zbMATHCrossRefMathSciNetADSGoogle Scholar
  30. 30.
    P. Gaspard, R. Kapral, G. Nicolis: J.Stat.Phys. 35, 697 (1984)zbMATHCrossRefMathSciNetADSGoogle Scholar
  31. 31.
    C. Sparrow: “The Lorenz equation”, AMS 41Google Scholar
  32. 32.
    P. Chossat, M. Golubitsky: Physica D 32, 423 (1988)zbMATHCrossRefADSMathSciNetGoogle Scholar
  33. 33.
    M. Dellnitz, M. Golubitsky, I. Melbourne: in E. Allgower, K. Böhmer, M. Golubitsky (Eds.): Bifurcation and Symmetry, Birkhäuser (1992)Google Scholar
  34. 34.
    Y. Pomeau, P. Manneville: Com.Math.Phys. 74, 189 (1980)CrossRefADSMathSciNetGoogle Scholar
  35. 35.
    J.E. Hirsch, B.A. Huberman, D.J. Scalapino: Phys.Rev.A 25, 319 (1982)CrossRefADSGoogle Scholar
  36. 36.
    P. Bergé, Y. Pomeau, C. Vidal: Order within chaos, Wiley (1984)Google Scholar
  37. 37.
    P. Bergé, M. Dubois, P. Manneville, Y. Pomeau: J.Physique-Lett. 41, L341 (1980)CrossRefGoogle Scholar
  38. 38.
    Chil-Min Kim, O.J. Kwon, Eok-Kyun Lee, Hoyun Lee: Phys.Rev.Lett 73, 525 (1994)CrossRefADSGoogle Scholar
  39. 39.
    M.O. Kim, Hoyun Lee, Chil-Min Kim, Hoyun-Soo Pang, Eok-Kyun Lee, O.J. Kwon: Int.J.Bif.Chaos 7, 831 (1997)CrossRefGoogle Scholar
  40. 40.
    M. Bauer, S. Habib, D.R. He, W. Martienssen: Phy.Rev.Lett 68, 1625(1992)zbMATHCrossRefADSGoogle Scholar
  41. 41.
    Pfister: in Proc. 4th Int. Conf. on Photon Correlation Techniques in Fluid Mech., Stanford CA (1980)Google Scholar
  42. 42.
    G.W. Baxter, C.D. Andereck: Phys.Rev.Lett. 57, 3046 (1986)CrossRefADSGoogle Scholar
  43. 43.
    J. Abshagen, A. Schulz, J. von Stamm, U. Gries, G. Pfister: in preparationGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Jan Abshagen
    • 1
  • Gerd Pfister
    • 1
  1. 1.Institute of Experimental and Applied PhysicsUniversity of KielKielGermany

Personalised recommendations