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Macroscopic Modelling of Turbulent Flows pp 296–303Cite as

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

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Part of the book series: Lecture Notes in Physics ((LNP,volume 230))

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References

  1. Y. Kuramoto, “Chemical oscillations, waves and turbulence” Springer Verlag Berlin, (1984).

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  2. G.I. Sivashinsky, Act. Astronautica 4, 1177 (1977); 6, 659 (1979).

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  3. B. Shraiman, D. Bensimon; Phys. Rev. A30, 2840 (1984).

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  4. A. Gervois, private communication

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  5. M.T. Aimar, These 3ème Cycle, Univ. Provence, Marseille, (1982).

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  6. B. Nikolaenko, B. Scheurer, R. Teman; to appear in Physica D.

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  7. A. Pumir, Y. Pomeau, P. Pelcé; J. of Stat. Phys. 37, 39 (1984).

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  8. A. Pumir, to appear in Phys. Rev. A.

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  9. See,for instance, A.J. Monin, A.M. Yaglom “Statistical Fluid Mechanics” M.I.T. Press (1972).

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  10. Communication at this Conference.

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  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.

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Authors and Affiliations

  1. CEN-Saclay, Service de Physique Théorique, 91191, Gif-sur Yvette Cedex, France

    Y. Pomeau

  2. Laboratoire de Physique de l'ENS, GPS 24 rue Lhomond, 75005, Paris, France

    Y. Pomeau & S. Zaleski

Authors
  1. Y. Pomeau
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  2. S. Zaleski
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Editor information

Uriel Frisch Joseph B. Keller George C. Papanicolaou Olivier Pironneau

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© 1985 Springer-Verlag

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Pomeau, Y., Zaleski, S. (1985). The Kuramoto-Sivashinsky equation : A caricature of hydrodynamic turbulence ?. In: Frisch, U., Keller, J.B., Papanicolaou, G.C., Pironneau, O. (eds) Macroscopic Modelling of Turbulent Flows. Lecture Notes in Physics, vol 230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-15644-5_23

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  • DOI: https://doi.org/10.1007/3-540-15644-5_23

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15644-4

  • Online ISBN: 978-3-540-39520-1

  • eBook Packages: Springer Book Archive

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