Quantum field renormalization group in the theory of fully developed turbulence

L.T. Adzhemyan^a, N.V. Antonov^a, A.N. Vasil’ev^a, b, c
^aDepartment of Theoretical Physics, Institute of Physics, St. Petersburg State University, ul. Ulyanovskaya 1, Petrodvorez, St. Petersburg, 198904, Russian Federation
^bLomonosov Moscow State University, Vorobevy Gory, Moscow, 119991, Russian Federation
^cLomonosov Moscow State University, Faculty of Physics, Leninskie Gory 1 build. 2, Moscow, 119991, Russian Federation

Quantum field renormalisation group results of the theory of developed turbulence are reviewed. Background information about quantum field renormalisation theory, including operator expansion and the renormalisation of composite operators is given. As an example problem, the stochastic model of isotropic homogeneous turbulence is considered for which, using the renormalisation technique, the existence of infrared scaling with Kholmogorov dimensions is proved. The dimension of composite operators and the infrared asymptotic behaviour of various correlation functions are discussed, and numerical amplitude factors of scaling laws are calculated.

PACS: 03.40.Ge, 47.10.+g
DOI: 10.1070/PU1996v039n12ABEH000183
URL: https://ufn.ru/en/articles/1996/12/a/
Web of Science

A1996WE26100001
Citation: Adzhemyan L T, Antonov N V, Vasil’ev A N "Quantum field renormalization group in the theory of fully developed turbulence" Phys. Usp. 39 1193–1219 (1996)

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Оригинал: Аджемян Л Ц, Антонов Н В, Васильев А Н «Квантово-полевая ренормализационная группа в теории развитой турбулентности» УФН 166 1257–1284 (1996); DOI: 10.3367/UFNr.0166.199612a.1257

References (122) Cited by (77) Similar articles (20) ↓

A.M. Bykov, I.N. Toptygin “Particle kinetics in highly turbulent plasmas (renormalization and self-consistent field methods)” 36 (11) 1020–1052 (1993)
N.M. Astaf’eva “Wavelet analysis: basic theory and some applications” 39 1085–1108 (1996)
L.M. Zelenyi, A.V. Milovanov “Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics” 47 749–788 (2004)
V.D. Buchel’nikov, A.N. Vasil’ev “Electromagnetic generation of ultrasound in ferromagnets” 35 (3) 192–211 (1992)
R.Kh. Zeytounian “The Benard-Marangoni thermocapillary-instability problem” 41 241–267 (1998)
I.V. Andreev “Chromodynamics as a theory of the strong interaction” 29 971–979 (1986)
A.N. Vasil’ev, V.D. Buchel’nikov et al “Shape memory ferromagnets” 46 559–588 (2003)
V.F. Gantmakher, V.T. Dolgopolov “Localized-delocalized electron quantum phase transitions” 51 3–22 (2008)
A.N. Vasil’ev, Yu.P. Gaidukov “Electromagnetic excitation of sound in metals” 26 952–973 (1983)
M.M. Markina, P.S. Berdonosov et al “Francisites as new geometrically frustrated quasi-two-dimensional magnets” 64 344–356 (2021)
Yu.A. Izyumov “Hubbard model of strong correlations” 38 385–408 (1995)
T.I. Belova, A.E. Kudryavtsev “Solitons and their interactions in classical field theory” 40 359–386 (1997)
K.L. Zarembo, Yu.M. Makeenko “An introduction to matrix superstring models” 41 1–23 (1998)
G.N. Sarkisov “Approximate equations of the theory of liquids in the statistical thermodynamics of classical liquid systems” 42 545–561 (1999)
V.V. Likhanskii, A.P. Napartovich “Radiation emitted by optically coupled lasers” 33 (3) 228–252 (1990)
V.A. Novikov “Nonperturbative QCD and supersymmetric QCD” 47 109–116 (2004)
V.L. Ginzburg, A.A. Sobyanin “Superfluidity of helium II near the λ point” 31 289–299 (1988)
A.A. Migdal “Stochastic quantization of field theory” 29 389–411 (1986)
V.S. Beskin, A.V. Gurevich, Ya.N. Istomin “Physics of pulsar magnetospheres” 29 946–970 (1986)
S.N. Gurbatov, A.I. Saichev, I.G. Yakushkin “Nonlinear waves and one-dimensional turbulence in nondispersive media” 26 857–876 (1983)

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