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Chaotic Behaviour in a Non-Linear System: Turbulence in Rayleigh Benard Convection

  • P. Bergé
Conference paper

Abstract

In this paper we will show that turbulent motions in confined convecting fluid are well understood in the frame of the theory of non-linear dynamical systems with a small number of degrees of freedom.

Keywords

Phase Space Rayleigh Number Chaotic Attractor Strange Attractor Chaotic Regime 
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Bibliography

  1. (1).
    P. Berge, Y. Pomeau and C. Vidal, Order within chaos (translated from l’ordre dans le chaos by L. Tuckerman) Wiley interscience Hermann (1986)Google Scholar
  2. (2).
    E. Ott, Strange attractors and chaotic motions of dynamical systems, Review of Modern Physics, 53, 655 (1981)CrossRefMATHADSMathSciNetGoogle Scholar
  3. (3).
    M.I. Rabinovich, Stochastic self-oscillations and turbulence, Soviet Physics Uspekhi, 21, 443 (1978)CrossRefADSGoogle Scholar
  4. (4).
    C. Normand, Y. Pomeau and M.G. Velarde, Convective instability: a physicist’s approach Review of Modern Physics 49, 581 (1977)ADSMathSciNetGoogle Scholar
  5. (5).
    P. Berge and M. Dubois, Rayleigh Benard Convection Contemporary Physics, 25, n°6 535 (1984)Google Scholar
  6. (6).
    J.P. Eckmann, Roads to turbulence in dissipative dynamical systems, Review of Modern Physics, 53, 643 (1981)CrossRefMATHADSMathSciNetGoogle Scholar
  7. (7).
    J.P. Gollub, S.V. Benson, Many routes to turbulent convection, Journal of Fluid Mechanics, 100, 449 (1980)CrossRefADSGoogle Scholar
  8. (8).
    M. Dubois and P. Bergé, Experimental evidence for the oscillators in a convective biperiodic regime, Physics Letters 76A, 53 (1980)CrossRefGoogle Scholar
  9. (9).
    M. Dubois and P. Bergé, Instabilité de couche limite dans un fluide en convection. Evolution vers la turbulence, Journal de Physique, 42, 167 (1981)Google Scholar
  10. (10).
    M. Dubois and P. Bergé, V. Croquette, Etude de régimes convectifs instationnaires à l’aide des diagrammes de Poincaré, Comptes Rendus dé l’Académie des Sciences de Paris, C293 409 (1981)Google Scholar
  11. (11).
    M. Dubois, Experimental aspects of the transition to turbulence in Rayleigh Benard convection in “Stability of Thermodynamic System”, Lecture Notes in Physics 164 177 (1981)Google Scholar
  12. (12).
    P. Bergé, Study of the phase space diagrams through experimental Poincaré sections in prechaotic and chaotic regimes, Physica Script Ti, 71 (1982)Google Scholar
  13. (13).
    F. Takens, in “Dynamical Systems and Turublence”, Lecture Notes in Mathematics 898 Springer Verlag, Berlin (1981)Google Scholar
  14. (14).
    P. Grassberger, I. Procaccia, Characterization of strange attractors, Physical Review Letters, 50, 346 (1983)CrossRefADSMathSciNetGoogle Scholar
  15. (15).
    B. Malraison, P. Atten, P. Bergé, M. Dubois, Dimension d’attracteurs étranges: une détermination expérimentale en régime chaotique de deux systèmes convectifs, Comptes Rendus de 1 ’ Académie des Sciences de Paris, C297 209 (1983)Google Scholar
  16. (16).
    A. Brandstäter, J. Swift, H.L. Swinney, A. Wolf, J.D. Farmer, E. Jen, J.P. Crutchfield, Low dimensional chaos in a system, Physical Review Letters, 51, 1442 (1983)CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • P. Bergé
    • 1
  1. 1.Service de Physique du Solide et de Résonance MagnétiqueCEN-SaclayGif-sur-Yvette CedexFrance

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