Standard

Renormalization group in the theory of turbulence : Three-loop approximation as d → ∞. / Adzhemyan, L. Ts; Antonov, N. V.; Gol'Din, P. B.; Kim, T. L.; Kompaniets, M. V.

In: Theoretical and Mathematical Physics, Vol. 158, No. 3, 01.03.2009, p. 391-405.

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

Harvard

Adzhemyan, LT, Antonov, NV, Gol'Din, PB, Kim, TL & Kompaniets, MV 2009, 'Renormalization group in the theory of turbulence: Three-loop approximation as d → ∞', Theoretical and Mathematical Physics, vol. 158, no. 3, pp. 391-405. https://doi.org/10.1007/s11232-009-0032-4

APA

Adzhemyan, L. T., Antonov, N. V., Gol'Din, P. B., Kim, T. L., & Kompaniets, M. V. (2009). Renormalization group in the theory of turbulence: Three-loop approximation as d → ∞. Theoretical and Mathematical Physics, 158(3), 391-405. https://doi.org/10.1007/s11232-009-0032-4

Vancouver

Adzhemyan LT, Antonov NV, Gol'Din PB, Kim TL, Kompaniets MV. Renormalization group in the theory of turbulence: Three-loop approximation as d → ∞. Theoretical and Mathematical Physics. 2009 Mar 1;158(3):391-405. https://doi.org/10.1007/s11232-009-0032-4

Author

Adzhemyan, L. Ts ; Antonov, N. V. ; Gol'Din, P. B. ; Kim, T. L. ; Kompaniets, M. V. / Renormalization group in the theory of turbulence : Three-loop approximation as d → ∞. In: Theoretical and Mathematical Physics. 2009 ; Vol. 158, No. 3. pp. 391-405.

BibTeX

@article{e05da8a7296e4433a05beacab14dc4a9,
title = "Renormalization group in the theory of turbulence: Three-loop approximation as d → ∞",
abstract = "We use the renormalization group method to study the stochastic Navier-Stokes equation with a random force correlator of the form k 4-d-2ε in a d-dimensional space in connection with the problem of constructing a 1/d-expansion and going beyond the framework of the standard ε-expansion in the theory of fully developed hydrodynamic turbulence. We find a sharp decrease in the number of diagrams of the perturbation theory for the Green's function in the large-d limit and develop a technique for calculating the diagrams analytically. We calculate the basic ingredients of the renormalization group approach (renormalization constant, β-function, fixed-point coordinates, and ultraviolet correction index ω) up to the order ε 3 (three-loop approximation). We use the obtained results to propose hypothetical exact expressions (i.e., not in the form of ε-expansions) for the fixed-point coordinate and the index ω.",
keywords = "Fully developed turbulence, Renormalization group",
author = "Adzhemyan, {L. Ts} and Antonov, {N. V.} and Gol'Din, {P. B.} and Kim, {T. L.} and Kompaniets, {M. V.}",
year = "2009",
month = mar,
day = "1",
doi = "10.1007/s11232-009-0032-4",
language = "English",
volume = "158",
pages = "391--405",
journal = "Theoretical and Mathematical Physics",
issn = "0040-5779",
publisher = "Springer Nature",
number = "3",

}

RIS

TY - JOUR

T1 - Renormalization group in the theory of turbulence

T2 - Three-loop approximation as d → ∞

AU - Adzhemyan, L. Ts

AU - Antonov, N. V.

AU - Gol'Din, P. B.

AU - Kim, T. L.

AU - Kompaniets, M. V.

PY - 2009/3/1

Y1 - 2009/3/1

N2 - We use the renormalization group method to study the stochastic Navier-Stokes equation with a random force correlator of the form k 4-d-2ε in a d-dimensional space in connection with the problem of constructing a 1/d-expansion and going beyond the framework of the standard ε-expansion in the theory of fully developed hydrodynamic turbulence. We find a sharp decrease in the number of diagrams of the perturbation theory for the Green's function in the large-d limit and develop a technique for calculating the diagrams analytically. We calculate the basic ingredients of the renormalization group approach (renormalization constant, β-function, fixed-point coordinates, and ultraviolet correction index ω) up to the order ε 3 (three-loop approximation). We use the obtained results to propose hypothetical exact expressions (i.e., not in the form of ε-expansions) for the fixed-point coordinate and the index ω.

AB - We use the renormalization group method to study the stochastic Navier-Stokes equation with a random force correlator of the form k 4-d-2ε in a d-dimensional space in connection with the problem of constructing a 1/d-expansion and going beyond the framework of the standard ε-expansion in the theory of fully developed hydrodynamic turbulence. We find a sharp decrease in the number of diagrams of the perturbation theory for the Green's function in the large-d limit and develop a technique for calculating the diagrams analytically. We calculate the basic ingredients of the renormalization group approach (renormalization constant, β-function, fixed-point coordinates, and ultraviolet correction index ω) up to the order ε 3 (three-loop approximation). We use the obtained results to propose hypothetical exact expressions (i.e., not in the form of ε-expansions) for the fixed-point coordinate and the index ω.

KW - Fully developed turbulence

KW - Renormalization group

UR - http://www.scopus.com/inward/record.url?scp=63849184171&partnerID=8YFLogxK

U2 - 10.1007/s11232-009-0032-4

DO - 10.1007/s11232-009-0032-4

M3 - Article

AN - SCOPUS:63849184171

VL - 158

SP - 391

EP - 405

JO - Theoretical and Mathematical Physics

JF - Theoretical and Mathematical Physics

SN - 0040-5779

IS - 3

ER -

ID: 36312942