Transition to Turbulence via Spatiotemporal Intermittency

  • H. Chaté
  • P. Manneville
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 43)


The study of low-dimensional dissipative dynamical systems has provided a reasonable understanding of the transition to temporal chaos in strongly confined systems for which the spatial structure can be considered as frozen. The situation is still less advanced for weakly confined systems where chaos has both a spatial and a temporal meaning. In order to approach the specificities of the latter, we have chosen to study first a partial differential equation (PDE) displaying a convective-type nonlinear term, steady cellular solutions as in convection, and a transition to spatiotemporal chaos, namely the damped Kuramoto-Sivashinsky (KS) equation:
$${\partial _t}\phi + \eta \phi + {\partial _{{x^2}}}\phi + {\partial _{{x^4}}}\phi + 2\phi {\partial _x}\phi = 0.$$


Directed Percolation Spatiotemporal Chaos Laminar State Probabilistic Cellular Automaton Probabilistic Cellular Automaton 
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.
    Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence ( Springer, Berlin, 1984 ).CrossRefMATHGoogle Scholar
  2. 2.
    J. Swift, P.C. Hohenberg, Phys.Rev. A15, 319 (1977).ADSGoogle Scholar
  3. 3a.
    Y. Pomeau, P. Manneville, Physics Lett. 75A, 296 (1980).CrossRefADSMathSciNetGoogle Scholar
  4. 3b.
    M.C. Cross, P.G. Daniels, P.C. Hohenberg, E.D. Siggia, J.Fluid Mech. 127, 155 (1983).CrossRefMATHADSMathSciNetGoogle Scholar
  5. 4.
    for a preliminary review of numerical results, see P. Manneville, AGARD (NATO) Special Course on Modern Theoretical and Experimental Approaches to Turbulent Flow Structure and its Modelling, report No.755 (Neuilly, 1987).Google Scholar
  6. 5.
    H. Chate, P. Manneville, Phys.Rev.Lett. 58, 112 (1987).CrossRefADSGoogle Scholar
  7. 6.
    Y. Pomeau, Physica 23D, 3 (1986).CrossRefGoogle Scholar
  8. 7a.
    K. Kaneko, Prog.Theor.Phys.74, 1033 (1985).Google Scholar
  9. 7b.
    G.-L. Oppo, R. Kapral, Phys.Rev. A33, 4219 (1986).ADSGoogle Scholar
  10. 7c.
    J.D. Keeler, D.J. Farmer, Physica 23D, 413 (1986).ADSMathSciNetGoogle Scholar
  11. 8.
    W. Kinzel, in Percolation Structures and Processes, Annals of the Israel Physical Society 5, 425 (1983).Google Scholar
  12. 9.
    H. Chate, P. Manneville, Physica D, in press.Google Scholar
  13. 10.
    W. Kinzel, Zeitschrift fur Physik B 58, 229 (1985).CrossRefMATHADSMathSciNetGoogle Scholar
  14. 11.
    H. Chate, P. Manneville, Europhysics Lett., in press.Google Scholar
  15. 12.
    H. Chate, P. Manneville, Proceedings of the 1988 annual meeting of CNLS to appear in Physica D.Google Scholar
  16. 13.
    D. Rochwerger, internal report, Ecole Poly technique, Palaiseau (1988); H. Chate, P. Manneville, D. Rochwerger, in preparation.Google Scholar
  17. 14.
    R. Bidaux, H.Chate, in preparation.Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1989

Authors and Affiliations

  • H. Chaté
    • 1
  • P. Manneville
    • 1
  1. 1.Institut de Recherche Fondamentale, DPh-G/PSRMCEN-SaclayGif-sur-YvetteFrance

Personalised recommendations