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A Simplified Theory of Intermittent Fully-Developed Turbulence

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Pattern Formation by Dynamic Systems and Pattern Recognition

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 5))

Abstract

Fully-developed turbulence consists of hierarchies of eddies of various sizes, where a small-scale eddy is generated from a larger eddy and disintegrates into smaller eddies of about the half-length size in a finite time. Using FRISCH-SULEM-NELKIN’s β-model of in-termittency in a slightly-extended form, we discuss how many eddies are generated from one eddy by the energy cascade. Let N be the mean number of offspring for one cascade step. For the β-model, the 1941 KOLMOGOROV theory leads to N=23, whereas a recent theory of FUJISAKA and MORI leads to N≃6.32. This number is related to the intermit-tency exponent µ by µ=3-log2N ≃0.341. This is in agreement with the experiments µexp =0.3~0.4.

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References

  1. A.S. Monin and A.M. Yaglom, Statistical Fluid Mechanics, Vol.2 (MIT Press, Cambridge, 1975) §21, §25.

    Google Scholar 

  2. E.A. Novikov and R.W. Stewart, Izv. Akad. Nauk SSSR, Ser. Geofis, no.3. (1964) 408.

    Google Scholar 

  3. A.M. Yaglom, Dokl. Akad. Nauk SSSR 166 (1966) 49

    Google Scholar 

  4. A.S. Gurvich and A.M. Yaglom, Phys. Fluids Suppl. (1967) S59.

    Google Scholar 

  5. R.H. Kraichnan, J. Fluid Mech. 62 (1974) 305.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. S.A. Orszag, in Fluid Dynamics ed. R. Balian and J.-L. Peube (Gordon & Breach, London, 1977) p.276.

    Google Scholar 

  7. U. Frisch, P.-L. Sulem and M. Nelkin, J. Fluid Mech. 87 (1978) 719 and references cited therein.

    Article  ADS  MATH  Google Scholar 

  8. A.M. Oboukhov, J. Fluid Mech. 13 (1962) 77.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. A.N. Kolmogorov, J. Fluid Mech. 13 (1962) 82.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. A.N. Kolmogorov, C.R. Acad. Sci. USSR 30 (1941) 301, 538. This is referred to as K41.

    Google Scholar 

  11. G.K. Batchelor and A.A. Townsend, Proc. Roy. Soc. A199 (1949) 238.

    ADS  Google Scholar 

  12. B.B. Mandelbrot, in Turbulence Seminar, Lecture Notes in Mathematics 615 (Springer-Verlag, Berlin, 1977); Fractals: Form, Chance and Dimension (Freeman, San Francisco, 1977).

    Google Scholar 

  13. For example, H. Haken, Synergetics (Springer-Verlag, Berlin, 1977) Chap.3.

    Google Scholar 

  14. H. Fujisaka and H. Mori, Prog. Theor. Phys. 62 (1979), No.1 (to be published).

    Google Scholar 

  15. A.S. Monin and A.M. Yaglom, ibid., pp.625–627 for a review of the experiments.

    Google Scholar 

  16. P.G. de Gennes, in Fluctuation, Instabilities and Phase Transitions ed. T. Riste (Plenum Press, New York, 1975).

    Google Scholar 

  17. M. Nelkin, Phys. Rev. A11 (1975) 1737.

    ADS  Google Scholar 

  18. S. Smale et al, Turbulence Seminar, Lecture Notes in Mathematics 615 (Springer-Verlag, Berlin, 1977).

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Physics, Kyushu University, Fukuoka 812, Japan

    H. Mori & H. Fujisaka

Authors
  1. H. Mori
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  2. H. Fujisaka
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Editor information

Editors and Affiliations

  1. Institut für Theoretische Physik der Universität Stuttgart, Pfaffenwaldring 57/IV, D-7000, Stuttgart 80, Fed. Rep. of Germany

    Hermann Haken

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Mori, H., Fujisaka, H. (1979). A Simplified Theory of Intermittent Fully-Developed Turbulence. In: Haken, H. (eds) Pattern Formation by Dynamic Systems and Pattern Recognition. Springer Series in Synergetics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-67480-8_8

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  • DOI: https://doi.org/10.1007/978-3-642-67480-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-67482-2

  • Online ISBN: 978-3-642-67480-8

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