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UFN, 1996, Volume 166, Number 12, Pages 1257–1284 (Mi ufn1269)  

This article is cited in 71 scientific papers (total in 71 papers)

REVIEWS OF TOPICAL PROBLEMS

Quantum field renormalization group in the theory of fully developed turbulence

L. Ts. Adzhemyan, N. V. Antonov, A. N. Vasil'ev

Saint-Petersburg State University

Abstract: 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.

DOI: https://doi.org/10.3367/UFNr.0166.199612a.1257

Full text: PDF file (5650 kB)
Full text: http://www.ufn.ru/ru/articles/1996/12/a/

English version:
Physics–Uspekhi, 1996, 39:12, 1193–1219

Bibliographic databases:

PACS: 03.40.Ge, 47.10.+g
Received: December 31, 1996

Citation: L. Ts. Adzhemyan, N. V. Antonov, A. N. Vasil'ev, “Quantum field renormalization group in the theory of fully developed turbulence”, UFN, 166:12 (1996), 1257–1284; Phys. Usp., 39:12 (1996), 1193–1219

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    This publication is cited in the following articles:
    1. N. V. Antonov, A. V. Runov, “Renormalization group in the theory of the two-dimensional turbulence: Instability of the fixed point with respect to weak anisotropy”, Theoret. and Math. Phys., 112:3 (1997), 1131–1139  mathnet  crossref  crossref  mathscinet  zmath  isi
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    3. L. Ts. Adzhemyan, N. V. Antonov, “Renormalization group in turbulence theory: Exactly solvable Heisenberg model”, Theoret. and Math. Phys., 115:2 (1998), 562–574  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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    5. Adzhemyan L., Hnatich M., Horvath D., Stehlik M., “Calculation of Spectra of Turbulence in the Energy-Containing and Inertial Ranges”, Phys. Rev. E, 58:4 (1998), 4511–4523  crossref  adsnasa  isi  scopus
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    13. Antonov N., “Anomalous Scaling of a Passive Scalar Advected by the Synthetic Compressible Flow”, Physica D, 144:3-4 (2000), 370–386  crossref  mathscinet  zmath  adsnasa  isi  scopus
    14. Antonov N., Lanotte A., Mazzino A., “Persistence of Small-Scale Anisotropies and Anomalous Scaling in a Model of Magnetohydrodynamics Turbulence”, Phys. Rev. E, 61:6, Part a (2000), 6586–6605  crossref  adsnasa  isi  scopus
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    26. Adzhemyan L., Honkonen J., Kompaniets M., Vasil'ev A., “Improved Epsilon Expansion for Three-Dimensional Turbulence: Summation of Nearest Dimensional Singularities”, Phys. Rev. E, 68:5, Part 2 (2003), 055302  crossref  mathscinet  adsnasa  isi  scopus
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    28. Adzhemyan L., Antonov N., Kompaniets M., Vasil'ev A., “Renormalization-Group Approach to the Stochastic Navier–Stokes Equation: Two-Loop Approximation”, Int. J. Mod. Phys. B, 17:10 (2003), 2137–2170  crossref  zmath  adsnasa  isi  scopus
    29. Cao Y., Chow W., “Renormalization Group Theory and its Application to Thermally-Induced Turbulence”, Commun. Theor. Phys., 41:4 (2004), 599–604  crossref  isi
    30. Hnatich M., Honkonen J., Jurcisin M., Mazzino A., Sprinc S., “Anomalous Scaling of Passively Advected Magnetic Field in the Presence of Strong Anisotropy”, Phys. Rev. E, 71:6, Part 2 (2005), 066312  crossref  adsnasa  isi  elib  scopus
    31. Adzhemyan L., Honkonen J., Kompaniets M., Vasil'ev A., “Improved Epsilon Expansion for Three-Dimensional Turbulence: Two-Loop Renormalization Near Two Dimensions”, Phys. Rev. E, 71:3, Part 2 (2005), 036305  crossref  mathscinet  adsnasa  isi  elib  scopus
    32. Adzhemyan L., Antonov N., Honkonen J., Kim T., “Anomalous Scaling of a Passive Scalar Advected by the Navier–Stokes Velocity Field: Two-Loop Approximation”, Phys. Rev. E, 71:1, Part 2 (2005), 016303  crossref  mathscinet  adsnasa  isi  elib  scopus
    33. Chkhetiani O.G., Hnatich M., Jurcisinova E., Jurcisin M., Mazzino A., Repasan M., “Influence of Helicity on Anomalous Scaling of a Passive Scalar Advected by the Turbulent Velocity Field with Finite Correlation Time: Two-Loop Approximation”, Phys. Rev. E, 74:3, Part 2 (2006), 036310  crossref  mathscinet  adsnasa  isi  elib  scopus
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    36. Antonov N., “Renormalization Group, Operator Product Expansion and Anomalous Scaling in Models of Turbulent Advection”, J. Phys. A-Math. Gen., 39:25 (2006), 7825–7865  crossref  zmath  adsnasa  isi  elib  scopus
    37. Antonov N., Hnatich M., Honkonen J., “Effects of Mixing and Stirring on the Critical Behaviour”, J. Phys. A-Math. Gen., 39:25 (2006), 7867–7887  crossref  zmath  adsnasa  isi  elib  scopus
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    40. Jurcisinova E., Jurcisin M., Remecky R., Scholtz M., “Combined Effects of Small Scale Anisotropy and Compressibility on Anomalous Scaling of a Passive Scalar”, Int. J. Mod. Phys. B, 22:21 (2008), 3589–3617  crossref  zmath  adsnasa  isi  elib  scopus
    41. Jurcisinova E., Jurcisin M., “Anomalous Scaling of a Passive Scalar Advected by a Turbulent Velocity Field with Finite Correlation Time and Uniaxial Small-Scale Anisotropy”, Phys. Rev. E, 77:1, Part 2 (2008), 016306  crossref  mathscinet  adsnasa  isi  elib  scopus
    42. E. Jurčišinová, M. Jurčišin, R. Remecky, M. Scholtz, “Numerical investigation of scaling regimes in a model of an anisotropically advected vector field”, Phys Part Nuclei Lett, 5:3 (2008), 219  crossref  zmath  adsnasa  scopus
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    47. Volchenkov D., “Renormalization Group and Instantons in Stochastic Nonlinear Dynamics”, Eur. Phys. J.-Spec. Top., 170 (2009), 1–142  crossref  isi  scopus
    48. Volchenkov D., “What Is Control of Turbulence in Crossed Fields?”, Commun. Nonlinear Sci. Numer. Simul., 15:2 (2010), 149–181  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
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