The Kuramoto-Sivashinsky equation : A caricature of hydrodynamic turbulence ?

  • Y. Pomeau
  • S. Zaleski
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 230)


Lyapunov Exponent Large Lyapunov Exponent Intrinsic Length Turbulent Behavior Hydrodynamic Turbulence 
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  1. [1]
    Y. Kuramoto, “Chemical oscillations, waves and turbulence” Springer Verlag Berlin, (1984).Google Scholar
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    G.I. Sivashinsky, Act. Astronautica 4, 1177 (1977); 6, 659 (1979).Google Scholar
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    B. Shraiman, D. Bensimon; Phys. Rev. A30, 2840 (1984).Google Scholar
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    A. Gervois, private communicationGoogle Scholar
  5. [5]
    M.T. Aimar, These 3ème Cycle, Univ. Provence, Marseille, (1982).Google Scholar
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    B. Nikolaenko, B. Scheurer, R. Teman; to appear in Physica D.Google Scholar
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    A. Pumir, Y. Pomeau, P. Pelcé; J. of Stat. Phys. 37, 39 (1984).Google Scholar
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    A. Pumir, to appear in Phys. Rev. A.Google Scholar
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    See,for instance, A.J. Monin, A.M. Yaglom “Statistical Fluid Mechanics” M.I.T. Press (1972).Google Scholar
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    Communication at this Conference.Google Scholar
  11. [11]
    If the diffusion coefficient \(D = \int_0^\infty {\overline {J(0)J(t)} } dt\) turns out to vanish, it may happens that the mean fourth power \(\overline {[Q(t)]^4 }\) becomes of order D′t at large times. Usually this fourth power is dominated by a term as 3D2t2. The coefficient D′ is a triple time integral of the four time correlation of J(.). In that case one might thus expect a similar growth of Q2 as t1/2 (instead of the more usual t), which would agree with our exponent 0.55 ±.05.Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Y. Pomeau
    • 1
    • 2
  • S. Zaleski
    • 2
  1. 1.CEN-SaclayService de Physique ThéoriqueGif-sur Yvette CedexFrance
  2. 2.Laboratoire de Physique de l'ENSParisFrance

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