N. V. Antonov, A. N. Vasil'ev, “Renormalization group in the theory of developed turbulence. The problem of justifying the Kolmogorov hypotheses for composite operators”, TMF, 110:1 (1997), 122–136; Theoret. and Math. Phys., 110:1 (1997), 97

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Teoreticheskaya i Matematicheskaya Fizika, 1997, Volume 110, Number 1, Pages 122–136
DOI: https://doi.org/10.4213/tmf957 (Mi tmf957)

This article is cited in 15 scientific papers (total in 15 papers)

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

N. V. Antonov, A. N. Vasil'ev

Saint-Petersburg State University

Full-text PDF (280 kB) Citations (15)

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DOI: https://doi.org/10.4213/tmf957

Abstract: Stohastic theory of fully developed turbulence is considered within the framework of the field theoretic renormalization group and short-distance expansion. The problem of verification of the Kolmogorov–Obukhov theory is discussed in connection with correlation functions of composite operators. An explicit expression for the critical dimensionality of a general composite operator is obtained. The Second Kolmogorov hypothesis (indepedence of the correlators on the viscosity) is proved for an arbitrary UV-finite composite operator. It is shown that there exists an infinite number of Galilean invariant scalar operators having negative critical dimensionalities.

Received: 21.05.1996

English version:
Theoretical and Mathematical Physics, 1997, Volume 110, Issue 1, Pages 97–108
DOI: https://doi.org/10.1007/BF02630373

Bibliographic databases:

Language: Russian

Citation: N. V. Antonov, A. N. Vasil'ev, “Renormalization group in the theory of developed turbulence. The problem of justifying the Kolmogorov hypotheses for composite operators”, TMF, 110:1 (1997), 122–136; Theoret. and Math. Phys., 110:1 (1997), 97–108

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf957

https://doi.org/10.4213/tmf957

https://www.mathnet.ru/eng/tmf/v110/i1/p122

This publication is cited in the following 15 articles:

Hnatic M. Honkonen J. Lucivjansky T., “Symmetry Breaking in Stochastic Dynamics and Turbulence”, Symmetry-Basel, 11:10 (2019), 1193
N. V. Antonov, M. Gnatich, A. S. Kapustin, T. Lučivjanský, L. Mižišin, “Directed-bond percolation subjected to synthetic compressible velocity fluctuations: Renormalization group approach”, Theoret. and Math. Phys., 190:3 (2017), 323–334
Antonov N.V. Gulitskiy N.M. Kostenko M.M. Lucivjansky T., “Turbulent compressible fluid: Renormalization group analysis, scaling regimes, and anomalous scaling of advected scalar fields”, Phys. Rev. E, 95:3 (2017), 033120
Hnatic M. Honkonen J. Lucivjansky T., “Advanced Field-Theoretical Methods in Stochastic Dynamics and Theory of Developed Turbulence”, Acta Phys. Slovaca, 66:2-3 (2016), 69–265
Antonov N.V. Kostenko M.M., “Anomalous Scaling of Passive Scalar Fields Advected By the Navier–Stokes Velocity Ensemble: Effects of Strong Compressibility and Large-Scale Anisotropy”, Phys. Rev. E, 90:6 (2014), 063016
L Ts Adzhemyan, N V Antonov, P B Gol'din, M V Kompaniets, “Anomalous scaling of a passive vector field inddimensions: higher order structure functions”, J. Phys. A: Math. Theor., 46:13 (2013), 135002
Adzhemyan L.T., Antonov N.V., Honkonen J., Kim T.L., “Anomalous scaling of a passive scalar advected by the Navier–Stokes velocity field: Two-loop approximation”, Phys. Rev. E (3), 71:1 (2005), 016303, 20 pp.
Adzhemyan L.Ts., Antonov N.V., Kompaniets M.V., Vasil'ev A.N., “Renormalization-group approach to the stochastic Navier–Stokes equation: two-loop approximation”, Int. J. Mod. Phys. B, 17:10 (2003), 2137–2170
Adzhemyan L.T., Antonov N.V., Hnatich M., Novikov S.V., “Anomalous scaling of a passive scalar in the presence of strong anisotropy”, Phys. Rev. E (3), 63:2 (2001), 016309
L. Ts. Adzhemyan, N. V. Antonov, M. Hnatich, S. V. Novikov, “Anomalous scaling of a passive scalar in the presence of strong anisotropy”, Phys. Rev. E, 63:1 (2000)
Antonov N.V., “Anomalous scaling regimes of a passive scalar advected by the synthetic velocity field”, Phys. Rev. E (3), 60:6 (1999), 6691–6707
Antonov N.V., Hnatich M., Nalimov M.Yu., “Influence of compressibility on scaling regimes of strongly anisotropic fully developed turbulence”, Phys. Rev. E (3), 60:4 (1999), 4043–4051
L. Ts. Adzhemyan, N. V. Antonov, “Renormalization group in turbulence theory: Exactly solvable Heisenberg model”, Theoret. and Math. Phys., 115:2 (1998), 562–574
Adzhemyan L.T., Antonov N.V., Vasil'ev A.N., “Renormalization group, operator product expansion, and anomalous scaling in a model of advected passive scalar”, Phys. Rev. E (3), 58:2, Part A (1998), 1823–1835
Adzhemyan L.Ts., Antonov N.V., Vasilev A.N., “Kvantovo-polevaya renormalizatsionnaya gruppa v teorii razvitoi turbulentnosti”, UFN, 166:12 (1996), 1257–1284

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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