This article is cited in 1 paper

Principle of maximal randomness and parity violation in turbulence

L. Ts. Adzhemyan^a, M. Gnatich^bc, M. V. Kompaniets<sup>a

a</sup> Saint Petersburg State University, St. Petersburg, Russia
^b Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia
^c P. J. Šafárik University in Košice, Košice

Abstract: 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, ultraviolet divergence.

DOI: 10.4213/tmf8469

 English version: Theoretical and Mathematical Physics, 2013, 176:1, 835–842

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