Standard

Renormalization group in the theory of two-dimensional turbulence : Instability of the fixed point with respect to weak anisotropy. / Antonov, N. V.; Runov, A. V.

In: Theoretical and Mathematical Physics, Vol. 112, No. 3, 09.1997, p. 1131-1139.

Research output: Contribution to journal › Article › peer-review

Harvard

Antonov, NV & Runov, AV 1997, 'Renormalization group in the theory of two-dimensional turbulence: Instability of the fixed point with respect to weak anisotropy', Theoretical and Mathematical Physics, vol. 112, no. 3, pp. 1131-1139. https://doi.org/10.1007/BF02583045

APA

Antonov, N. V., & Runov, A. V. (1997). Renormalization group in the theory of two-dimensional turbulence: Instability of the fixed point with respect to weak anisotropy. Theoretical and Mathematical Physics, 112(3), 1131-1139. https://doi.org/10.1007/BF02583045

Vancouver

Antonov NV, Runov AV. Renormalization group in the theory of two-dimensional turbulence: Instability of the fixed point with respect to weak anisotropy. Theoretical and Mathematical Physics. 1997 Sep;112(3):1131-1139. https://doi.org/10.1007/BF02583045

Author

Antonov, N. V. ; Runov, A. V. / Renormalization group in the theory of two-dimensional turbulence : Instability of the fixed point with respect to weak anisotropy. In: Theoretical and Mathematical Physics. 1997 ; Vol. 112, No. 3. pp. 1131-1139.

BibTeX

@article{b897af38737a4917a5fea30532029141,
title = "Renormalization group in the theory of two-dimensional turbulence: Instability of the fixed point with respect to weak anisotropy",
abstract = "A statistical model of fully developed turbulence in two-dimensional space is considered by means of the renormalization group method in the weak anisotropy approximation. It is shown that the corresponding fixed point of the renormalization group equations is not infrared stable. Hence, the weak anisotropy approximation is not valid for describing two-dimensional turbulence.",
author = "Antonov, {N. V.} and Runov, {A. V.}",
note = "Funding Information: One can easily find that one of the values (26) is negative for all e > 0, A _> 0. Therefore, the point (7) cannot be IR stable no matter how small the parameters Pl,2 are. From this, we conclude that the approximation of isotropic or weakly anisotropic turbulence is incorrect in the two-dimensional case for the model (4), (2) since, in this model, weak anisotropic perturbations become infinitely large in the IR asymptotic limit. The authors wish to thank L. Tz. Adzhemyan for the useful discussion. This work was performed under the support of the Russian Foundation for Basic Research (Grant. No. 96-02-17~?33) and the Competitive Center of Fundamental Natural Science, State Committee for Higher Education (Grant No. 95-0-5.1-30).",
year = "1997",
month = sep,
doi = "10.1007/BF02583045",
language = "English",
volume = "112",
pages = "1131--1139",
journal = "Theoretical and Mathematical Physics (Russian Federation)",
issn = "0040-5779",
publisher = "Springer Nature",
number = "3",

}

RIS

TY - JOUR

T1 - Renormalization group in the theory of two-dimensional turbulence

T2 - Instability of the fixed point with respect to weak anisotropy

AU - Antonov, N. V.

AU - Runov, A. V.

N1 - Funding Information: One can easily find that one of the values (26) is negative for all e > 0, A _> 0. Therefore, the point (7) cannot be IR stable no matter how small the parameters Pl,2 are. From this, we conclude that the approximation of isotropic or weakly anisotropic turbulence is incorrect in the two-dimensional case for the model (4), (2) since, in this model, weak anisotropic perturbations become infinitely large in the IR asymptotic limit. The authors wish to thank L. Tz. Adzhemyan for the useful discussion. This work was performed under the support of the Russian Foundation for Basic Research (Grant. No. 96-02-17~?33) and the Competitive Center of Fundamental Natural Science, State Committee for Higher Education (Grant No. 95-0-5.1-30).

PY - 1997/9

Y1 - 1997/9

N2 - A statistical model of fully developed turbulence in two-dimensional space is considered by means of the renormalization group method in the weak anisotropy approximation. It is shown that the corresponding fixed point of the renormalization group equations is not infrared stable. Hence, the weak anisotropy approximation is not valid for describing two-dimensional turbulence.

AB - A statistical model of fully developed turbulence in two-dimensional space is considered by means of the renormalization group method in the weak anisotropy approximation. It is shown that the corresponding fixed point of the renormalization group equations is not infrared stable. Hence, the weak anisotropy approximation is not valid for describing two-dimensional turbulence.

UR - http://www.scopus.com/inward/record.url?scp=0031322344&partnerID=8YFLogxK

U2 - 10.1007/BF02583045

DO - 10.1007/BF02583045

M3 - Article

AN - SCOPUS:0031322344

VL - 112

SP - 1131

EP - 1139

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 3

ER -

ID: 86533966