Abstract:
The stochastic theory of the developed turbulence is considered with the random force correlator of the form $k(k^2+m^2)^{-\varepsilon}$, $m$ being the inverse large turbulent scale. The first Kolmogorov hypothesis (i.e., finiteness of the equal time correlator of velocities at $\varepsilon<2$) is justified using the Wilson's operator product expansion.
Citation:
N. V. Antonov, “On the infrared asymptotics of the velocity-velocity correlator in the theory of the turbulence”, Questions of quantum field theory and statistical physics. Part 10, Zap. Nauchn. Sem. LOMI, 189, Nauka, St. Petersburg, 1991, 15–23; J. Soviet Math., 62:5 (1992), 2950–2955
\Bibitem{Ant91}
\by N.~V.~Antonov
\paper On the infrared asymptotics of the velocity-velocity correlator in the theory of the turbulence
\inbook Questions of quantum field theory and statistical physics. Part~10
\serial Zap. Nauchn. Sem. LOMI
\yr 1991
\vol 189
\pages 15--23
\publ Nauka
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4879}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1111673}
\zmath{https://zbmath.org/?q=an:0783.76046|0744.76067}
\transl
\jour J. Soviet Math.
\yr 1992
\vol 62
\issue 5
\pages 2950--2955
\crossref{https://doi.org/10.1007/BF01097494}
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https://www.mathnet.ru/eng/znsl4879
https://www.mathnet.ru/eng/znsl/v189/p15
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