Hydrodynamic Instability: Structure and Chaos

  • Jean-Pierre Boon
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 73)


It is about one century ago that Reynolds investigated hydro-dynamic transitions in pipe and channel flows; active work in this area of fluid dynamics has been pursued continuously since. Yet turbulence which appears as the ultimate stage of hydrodynamic flow remains one of the puzzling problems of classical physics. Turbulence manifests itself by chaotic behavior; developped turbulence is characterized by complete loss of spatial and temporal correlations and by its extreme sensitivity to initial conditions. Fully developed turbulence as it appears in flows past an obstacle is probably the most familiar example of turbulent flow;1 it is also the most complex and least well understood case of turbulence. It involves the excitation of a very large number of degrees of freedom according to Landau’s 1944 original picture of turbulence.2


Rayleigh Number Chaotic Behavior Fluid Layer Strange Attractor Convective Velocity 
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  1. 1.
    R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures in Physics, (Addison-Wesley, Reading, MA, 1964). Vol. II, Chapter 40.Google Scholar
  2. 2.
    L. D. Landau, and E. M. Lifschitz, Fluid Mechanics, (Pergamon Press, 1959). Chapter 3.Google Scholar
  3. 3.
    E. N. Lorenz, J. Atmosp. Sci. 20: 448 (1963).ADSCrossRefGoogle Scholar
  4. 4.
    D. Ruelle, and F. Takens, Comm. Math. Phys. 20: 167 (1971).MathSciNetADSMATHCrossRefGoogle Scholar
  5. 5.
    G. Ahlers, Phys. Rev. Lett. 33: 1185 (1974).ADSCrossRefGoogle Scholar
  6. 6.
    J. P. Gollub, and H. L. Swinney, Phys. Rev. Lett. 35: 927 (1975).ADSCrossRefGoogle Scholar
  7. 7.
    P. Berge, and M. Dubois, Optics Comm. 19: 129 (1976).ADSCrossRefGoogle Scholar
  8. 8.
    G. Ahlers, and P.P. Behringer, Phys. Rev. Lett.040: 712 (1978).ADSCrossRefGoogle Scholar
  9. 9.
    A. Libchaber, and J. Maurer, J. Phys. Lett. 39: L-369 (1978).Google Scholar
  10. 10.
    J. B. McLaughlin, and P. C. Martin, Phys. Rev. A12: 186 (1975).ADSGoogle Scholar
  11. 11.
    P. Coullet, Ph.D. Thesis, University of Nice (1980) and reference therein.Google Scholar
  12. 12.
    V. Degiorgio, Phys. Rev. A20; 2193 (1979).ADSGoogle Scholar
  13. 13.
    J. P. Gollub, and M. H. Frielich, Phys. Rev. Lett. 33: 1465 (1974).ADSCrossRefGoogle Scholar
  14. 14.
    P. Berge, and M. Dubois, in the present volume.Google Scholar
  15. 15.
    G. Nicolis, and I. Prigogine, Self-Organization in Nonequili-brium Systems, (Springer-Verlag, Berlin, 1977).Google Scholar
  16. 16.
    For an introduction to the problem of convection, see M. G. Velarde, and C. Normand, Sci. Amer. 243: 79 (1980).Google Scholar
  17. 17.
    S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, (Oxford University Press, 1961). Chapter 2.MATHGoogle Scholar
  18. 18.
    H. N. W. Lekkerkerker, and J. P. Boon, Phys. Rev. A10: 1355 (1974).ADSGoogle Scholar
  19. 19.
    V. M. Zaitsev, and M. I. Shliomis, Sov. Phys. JETP 32: 866 (1971).ADSGoogle Scholar
  20. 20.
    B. J. Berne, and R. Pécora, Dynamic Light Scattering, (Wiley-Interscience, New York, 1976). Chapter 10.Google Scholar
  21. 21.
    J. P. Boon, and P. Deguent, Phys. Lett. A39: 315 (1972).ADSGoogle Scholar
  22. 22.
    J. B. Lastovka, Bell. Syst. Tech. J. 55: 1225 (1976).Google Scholar
  23. 23.
    D. W. Pohl, IBM J. 23: 605 (1979).CrossRefGoogle Scholar
  24. 24.
    C. Allain, H. Z. Cummins, and P. Lallemand, J. Phys. Lett. 39: L-473 (1978).CrossRefGoogle Scholar
  25. 25.
    J. Weisfreid, P. Berge, and M. Dubois, Phys. Rev. A19: 1231 (1979).ADSGoogle Scholar
  26. 26.
    A more complete discussion of pretransitional phenomena is given by the author in “Les Instabilités Hydrodynamiques”, (Springer Verlag, Heidelberg, 1978).Google Scholar
  27. 27.
    G. Z. Gershuni, and E. M. Zhukovitskii, Convection Stability of Incompressible Fluids, (Keter Publishing House, Jerusalem, 1976). Chapter 1.Google Scholar
  28. 28.
    J. P. Boon, C. Allain, and P. Lallemand, Phys. Rev. Lett. 43: 199 (1979).ADSCrossRefGoogle Scholar
  29. 29.
    P. G. Simpkins, and T. D. Dudderar, J. Fluid Mech. 89: 665 (1978);ADSCrossRefGoogle Scholar
  30. 29a.
    R. Meynart, Applied Optics Lett. 19: 1385 (1980).ADSCrossRefGoogle Scholar
  31. 30.
    J. P. Gollub, and M. H. Freilich, Phys. Rev. Lett. 33: 1465 (1974).ADSCrossRefGoogle Scholar
  32. 31.
    H. L. Swinney, and J. P. Gollub, Phys. Today 31: 41 (1978), and references therein.CrossRefGoogle Scholar
  33. 32.
    M. Dubois, and P. Berge, J. Fluid Mech. 85: 641 (1978).ADSCrossRefGoogle Scholar
  34. 33.
    P. C. Martin, in “Proceedings of the International Conference on Statistical Physics” (North Holland, Amsterdam, 1975).Google Scholar
  35. 34.
    C. Baesens, M. D. Thesis (University of Brussels, 1980).Google Scholar
  36. 35.
    H. L. Swinney, Prog. Theor. Phys. Suppl. 64: 164 (1978);ADSCrossRefGoogle Scholar
  37. 35a.
    J. Maurer and A. Libchaber, J. Physique Lett. 40: L-419 (1979);CrossRefGoogle Scholar
  38. 35b.
    G. Ahlers, in “Systems Far From Equilibrium” (Springer-Verlag, Heidelberg, 1980);Google Scholar
  39. 35c.
    M. Dubois, Colloque P. Curie, to be published in J. Physique.Google Scholar
  40. 36.
    M. Dubois, and P. Berge, to appear in J. Physique.Google Scholar
  41. 37.
    L. N. Howard, in “Proceedings of the 11th International Conference of Applied Mechanics”, (Springer-Verlag, Heidelberg, 1966). p. 1109.Google Scholar
  42. 38.
    P. Berge, and Y. Pomeau, La Recherche, 11: 422 (1980).Google Scholar
  43. 39.
    J. C. Roux, A. Rossi, S. Bachelart, and C. Vidal, Phys. Lett. 77A (1980).Google Scholar
  44. 40.
    J. P. GoHub, and S. Benson, Phys. Rev. Lett. 41: 948 (1978).ADSCrossRefGoogle Scholar
  45. 41.
    G. Ahlers, and R. P. Behringer, Prog. Theor. Phys. Suppl. 64: 186 (1978).ADSCrossRefGoogle Scholar
  46. 42.
    P. R. Fenstermacher, H. L. Swinney, and J. P. Gollub, J. Fluid Mech. 94: 103 (1979).ADSCrossRefGoogle Scholar
  47. 43.
    M. Gorman, and H. L. Swinney, Phys. Rev. Lett. 43: 1871 (1979).ADSCrossRefGoogle Scholar
  48. 44.
    P. Coullet, C. Tresser, and A. Arneodo, Phys. Lett. 77A: 327 (1980).MathSciNetADSGoogle Scholar
  49. 45.
    P. Berge, M. Dubois, P. Manneville, and Y. Pomeau, J. Physique Lett. 41: L-341 (1980).CrossRefGoogle Scholar
  50. 46.
    M. Dubois, Communication at the “Colloque Pierre Curie” (Paris, 1980), to be published in J. Physique.Google Scholar
  51. 47.
    P. Manneville, and Y. Pomeau, Phys. Lett. 75A: 1 (1979).MathSciNetADSGoogle Scholar
  52. 48.
    J. P. Gollub, and S. Benson, to be published (1980).Google Scholar
  53. 49.
    A. Libchaber, and J. Maurer, J. Physique C-3: 41 (1980).Google Scholar
  54. 50.
    M. J. Feigenbaum, Phys. Lett. 74A: 375 (1979).MathSciNetADSGoogle Scholar

Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • Jean-Pierre Boon
    • 1
    • 2
  1. 1.Faculté des SciencesUniversité Libre de BruxellesBruxellesBelgium
  2. 2.Physique de la Matière CondenséeUniversité de NiceNiceFrance

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