Comptes Rendus
Extension of the Kida law in turbulence
Comptes Rendus. Mécanique, Volume 331 (2003) no. 11, pp. 775-782.

We extend the validity range of Kida's log-stable law of stability index α=1.65 and intermittency parameter μ=0.2 to a new range of Reynolds number. This law describes intermittencies in fully developed turbulent flows or more precisely the p.d.f. of turbulence dissipation. Former measurements of the hyper-flatness factors of order 4, 5, 6 of turbulent velocity increments, coming from both experimental works and numerical simulations are used. We show that the power-law variation of these hyper-flatness factors with Taylor scale based Reynolds numbers Reλ can be fitted, for Reλ ranging from 35 to 750, by a log-stable law of stability index α=1.65 and intermittency parameter μ=0.21.

On étend le domaine de validité de la loi de Kida d'indice de stabilité α=1,65 et de paramètre d'intermittence μ=0,2 à une nouvelle gamme de nombre de Reynolds. Cette loi décrit les intermittences en turbulence pleinement développée ou plus précisément la distribution de densité de probabilité de la dissipation de la turbulence. On utilise les résultats des mesures des coefficients d'hyper-aplatissement d'ordre 4, 5 et 6 des incréments de vitesse turbulente issues de précédentes études expérimentales et numériques. Nous montrons que la variation en loi de puissance de ces coefficients avec le nombre de Reynolds construit sur la micro-échelle de Taylor λ peut être ajustée pour Reλ compris entre 35 et 750 à l'aide d'une loi log-stable d'indice de stabilité α=1,65 et de paramètre d'intermittence μ=0,21.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-0721(03)00143-8
Keywords: Turbulence, Intermittency, Cascade theory, Log-stable law
Mot clés : Turbulence, Intermittence, Théorie de la cascade, Distribution log-Lévy

Nicolas Rimbert 1; Olivier Séro-Guillaume 1

1 LEMTA, INPL-UHP-CNRS, 2, av. de la Forêt de Haye, 54504 Vandoeuvre cedex, France
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Nicolas Rimbert; Olivier Séro-Guillaume. Extension of the Kida law in turbulence. Comptes Rendus. Mécanique, Volume 331 (2003) no. 11, pp. 775-782. doi : 10.1016/S1631-0721(03)00143-8. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00143-8/

[1] S. Kida Log-stable distribution and intermittency of turbulence, J. Phys. Soc. Japan, Volume 60 (1991) no. 1, pp. 5-8

[2] A.M. Oboukhov Some specific features of atmospheric turbulence, J. Fluid Mech., Volume 13 (1961), pp. 77-81

[3] A.N. Kolmogorov A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number, J. Fluid Mech., Volume 13 (1962), pp. 82-85

[4] A.N. Kolmogorov On the logarithmically normal law of distribution of the size of particles under pulverization, Dokl. Akad. Nauk SSSR, Volume 31 (1941), pp. 99-101

[5] E.A. Novikov Infinitely divisible distributions in turbulence, Phys. Rev. E, Volume 50 (1994), pp. 50-52

[6] B. Castaing; B. Dubrulle Fully developed turbulence: a unifying point of view, J. Phys. II (France), Volume 5 (1995), pp. 895-899

[7] D. Schertzer; S. Lovejoy; F. Schmitt; Y. Chiguirinskaya; D. Marsan Multifractal cascade dynamics and turbulent intermittency, Fractals, Volume 5 (1997) no. 3, pp. 427-471

[8] F. Anselmet; Y. Gagne; E.J. Hopfinger; R.A. Antonia High-order velocity structure function in turbulent shear flows, J. Fluid Mech., Volume 140 (1984) no. 63

[9] S. Kida Log-stable distribution in turbulence, Fluid Dyn. Res., Volume 8 (1991), pp. 135-138

[10] R.W. Stewart; J.R. Wilson; R.W. Burling Some statistical properties of small scale turbulence in an atmospheric boundary layer, J. Fluid Mech., Volume 41 (1970), pp. 141-152

[11] R.M. Kerr Higher-order derivative correlations and the alignment of small-scale structure in isotropic numerical turbulence, J. Fluid Mech., Volume 153 (1985), pp. 31-58

[12] F. Belin; J. Maurer; P. Tabeling; H. Willaime Velocity gradient distributions in fully developed turbulence: an experimental study, Phys. Fluids, Volume 9 (1997) no. 12, pp. 3843-3850

[13] P. Tabeling; H. Willaime Transition at dissipative scales in large-Reynolds-number turbulence, Phys. Rev. E, Volume 65 (2002), p. 066301

[14] G. Samorodnitsky; M.S. Taqqu Stable Non-Gaussian Random Processes, Chapman & Hall, 1994

[15] A.S. Monin; A.M. Yaglom, Statistical Fluid Mechanics, 2, MIT Press, 1987

[16] H. Tennekes; J.L. Lumley A First Course in Turbulence, MIT Press, 1972

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