Geodesic
Principle of maximal randomness and parity violation in turbulence
Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 1, pp. 3-12 Cet article a éte moissonné depuis la source Math-Net.Ru

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We show that in the self-consistent equations for equal-time correlation functions of velocity fluctuations obtained in the model of developed turbulence based on the maximal randomness principle, infrared divergences are absent from all orders of the perturbation theory. We analyze the additional ultraviolet (UV) divergences that appear in the two-loop approximation of the self-consistent equations. We show that in the system with conserved parity, these divergences can be eliminated using the existing ambiguity in the solution. In the case of parity violation in the system, the UV divergences have a logarithmic form, which can indicate a deviation from the Kolmogorov scaling.
Keywords: self-consistency equation, Kolmogorov power law, helicity, parity violation, infrared divergence
Mots-clés : ultraviolet divergence. 
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L. Ts. Adzhemyan; M. Gnatich; M. V. Kompaniets. Principle of maximal randomness and parity violation in turbulence. Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 1, pp. 3-12. http://geodesic.mathdoc.fr/item/TMF_2013_176_1_a0/

[1] A. S. Monin, A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence, Dover, Mineola, NY, 2007 | MR | MR | Zbl

[2] E. Kit, A. Tsinober, J. L. Balint, J. M. Wallace, E. Levich, Phys. Fluids, 30:11 (1987), 3323–3325 | DOI

[3] J. M. Wallace, J.-L. Balint, L. Ong, Phys. Fluids A, 4:9 (1992), 2013, 14 pp. | DOI

[4] M. Thiele, W.-C. Müller, J. Fluid Mech., 637 (2009), 425–442, arXiv: 0906.0853 | DOI | Zbl

[5] C. Morize, F. Moisy, Phys. Fluids, 18:6 (2006), 065107, 9 pp. | DOI | MR | Zbl

[6] Y. Morinishi, K. Nakabayashi, S. Q. Ren, Phys. Fluids, 13:10 (2001), 2912–2922 | DOI | Zbl

[7] L. Ts. Adzhemyan, M. Hnatich, M. Stehlik, J. Phys. II France, 5:7 (1995), 1077–1092 | DOI

[8] S. F. Edwards, W. D. McComb, J. Phys. A, 2:2 (1969), 157–171 | DOI | Zbl

[9] A. Yoshizawa, J. Phys. Soc. Japan, 40:5 (1976), 1498–1503 | DOI | MR | Zbl

[10] A. A. Migdal, Modern Phys. Lett. A, 6:11 (1991), 1023–1043 | DOI | MR | Zbl

[11] A. N. Vasilev, Kvantovopolevaya renormgruppa v teorii kriticheskogo povedeniya i stokhasticheskoi dinamike, Izd-vo PIYaF, SPb., 1998 | MR