Research output: Contribution to journal › Article › peer-review
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
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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 (Russian Federation)
JF - Theoretical and Mathematical Physics (Russian Federation)
SN - 0040-5779
IS - 3
ER -
ID: 36312942