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Transition to Turbulence via Spatiotemporal Intermittency

  • Conference paper
Cooperative Dynamics in Complex Physical Systems

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 43))

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Abstract

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:

$${\partial _t}\phi + \eta \phi + {\partial _{{x^2}}}\phi + {\partial _{{x^4}}}\phi + 2\phi {\partial _x}\phi = 0.$$
((1))

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References

  1. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence ( Springer, Berlin, 1984 ).

    Book  MATH  Google Scholar 

  2. J. Swift, P.C. Hohenberg, Phys.Rev. A15, 319 (1977).

    ADS  Google Scholar 

  3. Y. Pomeau, P. Manneville, Physics Lett. 75A, 296 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  4. M.C. Cross, P.G. Daniels, P.C. Hohenberg, E.D. Siggia, J.Fluid Mech. 127, 155 (1983).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. 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. H. Chate, P. Manneville, Phys.Rev.Lett. 58, 112 (1987).

    Article  ADS  Google Scholar 

  7. Y. Pomeau, Physica 23D, 3 (1986).

    Article  Google Scholar 

  8. K. Kaneko, Prog.Theor.Phys.74, 1033 (1985).

    Google Scholar 

  9. G.-L. Oppo, R. Kapral, Phys.Rev. A33, 4219 (1986).

    ADS  Google Scholar 

  10. J.D. Keeler, D.J. Farmer, Physica 23D, 413 (1986).

    ADS  MathSciNet  Google Scholar 

  11. W. Kinzel, in Percolation Structures and Processes, Annals of the Israel Physical Society 5, 425 (1983).

    Google Scholar 

  12. H. Chate, P. Manneville, Physica D, in press.

    Google Scholar 

  13. W. Kinzel, Zeitschrift fur Physik B 58, 229 (1985).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. H. Chate, P. Manneville, Europhysics Lett., in press.

    Google Scholar 

  15. H. Chate, P. Manneville, Proceedings of the 1988 annual meeting of CNLS to appear in Physica D.

    Google Scholar 

  16. D. Rochwerger, internal report, Ecole Poly technique, Palaiseau (1988); H. Chate, P. Manneville, D. Rochwerger, in preparation.

    Google Scholar 

  17. R. Bidaux, H.Chate, in preparation.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institut de Recherche Fondamentale, DPh-G/PSRM, CEN-Saclay, F-91191, Gif-sur-Yvette, France

    H. Chaté & P. Manneville

Authors
  1. H. Chaté
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  2. P. Manneville
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Editor information

Editors and Affiliations

  1. Research Institute for Fundamental Physics, (Yukawa Hall), Kyoto University, Kyoto, 606, Japan

    Hajime Takayama

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© 1989 Springer-Verlag Berlin, Heidelberg

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Chaté, H., Manneville, P. (1989). Transition to Turbulence via Spatiotemporal Intermittency. In: Takayama, H. (eds) Cooperative Dynamics in Complex Physical Systems. Springer Series in Synergetics, vol 43. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-74554-6_75

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  • DOI: https://doi.org/10.1007/978-3-642-74554-6_75

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-74556-0

  • Online ISBN: 978-3-642-74554-6

  • eBook Packages: Springer Book Archive

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