TY - JOUR

T1 - Renormalization group in the theory of developed turbulence. The problem of justifying the Kolmogorov hypotheses for composite operators

AU - Antonov, N. V.

AU - Vasil’ev, A. N.

N1 - Funding Information: Thus, the main problems remaining in the 1RG theory of turbulence are the explicit constructi~m ,)f all "dangerous" invariant operators, c~th:ulation of their critical dimensions, ~md summat, i(m ~d their contritmt.ions in operator expansions in order to investigate the asymptotic behavior as ii~ ~ 1) aml t~ verify Hypothesis 1 of Kohnogorov. Clearly, the solution of all of these problems require c(msid~'r;d~h' improvement of the existing methods. This work was p~q'tbrmed under the financial support of the Russian Foundati(m t'()r Basic' lr (t)ro.je('t No. 96-02-17-033) and the Competitive Center for Basic Natural Science of th+, State ('~)llllllill(',' f~)r High('r Education (Pr%}(,ct No. 95-0-5.1-30).

PY - 1997/1

Y1 - 1997/1

N2 - In this paper, the stochastic theory of developed turbulence is considered within the framework of the quantum field renormalization group and operator expansions. The problem of justifying the Kolmogorov-Obukhov theorem in application to the correlation functions of composite operators is discussed. An explicit expression is found for the critical dimension of a general-type composite operator. For an arbitrary UV-finite composite operator, the second Kolmogorov hypothesis (the viscosity-independence of the correlator) is proved and the dependence of various correlators on the external turbulence scale is determined. It is shown that the problem involves an infinite number of Galilean-invariant scalar operators with negative critical dimensions.

AB - In this paper, the stochastic theory of developed turbulence is considered within the framework of the quantum field renormalization group and operator expansions. The problem of justifying the Kolmogorov-Obukhov theorem in application to the correlation functions of composite operators is discussed. An explicit expression is found for the critical dimension of a general-type composite operator. For an arbitrary UV-finite composite operator, the second Kolmogorov hypothesis (the viscosity-independence of the correlator) is proved and the dependence of various correlators on the external turbulence scale is determined. It is shown that the problem involves an infinite number of Galilean-invariant scalar operators with negative critical dimensions.

UR - http://www.scopus.com/inward/record.url?scp=0031483188&partnerID=8YFLogxK

U2 - 10.1007/BF02630373

DO - 10.1007/BF02630373

M3 - Article

AN - SCOPUS:0031483188

VL - 110

SP - 97

EP - 108

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 1

ER -