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Prog. Theor. Phys. Vol. 62 No. 1 (1979) pp. 54-60

[ Full Text PDF : FREE ACCESS (512K) ]

A Maximum Principle for Determining the Intermittency Exponent µ of Fully Developed Steady Turbulence

Hirokazu Fujisaka and Hazime Mori

Department of Physics, Kyushu University, Fukuoka 812

(Received March 7, 1979)

Abstract:

The energy spectrum in the inertial range takes the form E(k) ∝ε2/3k-5/3(kl0)-B, where ε is the mean rate of energy transfer and l0 is the length scale of the production range. The β-model of intermittency presented by Frisch, Sulem and Nelkin (1978), leads to the Mandelbrot relation B=µ/3(3-D)/3, where D is a fractional dimension.
A new statistical hypothesis on the energy cascade is introduced determine the exponent D. The vortex-stretching picture implies that vortices change into thinner, more extended ribbon-like structures, eventually producing a random spatial distribution of eddies of different sizes. With the aid of this picture, an information entropy of intermittency H(D) is defined and is assumed to take a maximum value in the steady state. This determines D. In fact, an explicit expression for H(D) is derived for the β-model and the maximum principle is shown to give µ= 0.34, D=2.66 in agreement with the experiments µ=0.3 ∼0.5. The mean number of offspring for one cascade step turns out to be 6.32.


URL : http://ptp.ipap.jp/link?PTP/62/54/
DOI : 10.1143/PTP.62.54

[ Full Text PDF : FREE ACCESS (512K) ] Citation:

References:

  1. B. B. Mandelbrot, in Fluid Dynamics, ed. by R. Balian and J. L. Peube (Gordon and Breach, London, 1977); Fractals: Form, Chance and Dimension (Freeman, San Francisco, 1977).
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  11. M. Nelkin, “Universality and Scaling in Fully Developed Turbulence,” Proceedings of the 13th International Conference on Statistical Physics (Haifa, Israel, 1977).

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 63 No. 3 (1980) pp. 1044-1047 :
    Fractal Dimensions of Chaotic Flows of Autonomous Dissipative Systems
    Hazime Mori
  2. Progress of Theoretical Physics Vol. 63 No. 6 (1980) pp. 1931-1944 :
    Statistical Dynamics of Chaotic Flows
    Hazime Mori and Hirokazu Fujisaka
  3. Progress of Theoretical Physics Vol. 67 No. 5 (1982) pp. 1630-1632 :
    Statistics of Active Regions in the β-Model of Turbulence
    Shigeo Kida
  4. Progress of Theoretical Physics Vol. 68 No. 2 (1982) pp. 439-447 :
    Diffusion of Particles in Fully-Developed Turbulence
    Kiyofumi Takayoshi and Hazime Mori
  5. Progress of Theoretical Physics Vol. 68 No. 6 (1982) pp. 2180-2183 :
    On the β-Model of Intermittent Fully-Developed Turbulence
    Hazime Mori and Hirokazu Fujisaka
  6. Progress of Theoretical Physics Vol. 69 No. 3 (1983) pp. 725-741 :
    Vortex Stretching and Relative Diffusion in Grid Turbulence
    Hazime Mori and Kiyofumi Takayoshi
  7. Progress of Theoretical Physics Vol. 69 No. 3 (1983) pp. 756-772 :
    Enstrophy Cascade and Relative Diffusion in Two-Dimensional Fully-Developed Turbulence
    Hazime Mori
  8. Progress of Theoretical Physics Vol. 70 No. 4 (1983) pp. 961-974 :
    Time Evolution of Fully-Developed Turbulence
    Kiyofumi Takayoshi and Hazime Mori
  9. Progress of Theoretical Physics Vol. 70 No. 5 (1983) pp. 1183-1196 :
    Intermittency and Relative Diffusion in Fully-Developed Turbulence
    Hazime Mori and Kiyofumi Takayoshi
  10. Progress of Theoretical Physics Vol. 73 No. 3 (1985) pp. 586-597 :
    Fluctuations in Processes of Phase-Separations and Intermittent Droplet Growth
    Hiroshi Furukawa
  11. Progress of Theoretical Physics Vol. 73 No. 5 (1985) pp. 1141-1150 :
    1/f Noise and Turbulence from a Self-Similar Decay of Fluctuation
    Hiroshi Furukawa
  12. Progress of Theoretical Physics Vol. 75 No. 6 (1986) pp. 1295-1303 :
    The Scaling Exponents of Intermittent Fully Developed Turbulence Based on a New Model
    Tohru Nakano
  13. Progress of Theoretical Physics Supplement No.69 (1980) pp. 111-121 :
    Anomalous Diffusion of Vorticity in Fully-Developed Turbulence
    Hazime Mori

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