Geodesic
Renormalization group in the theory of turbulence: Three-loop approximation as $d\to\infty$
Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 3, pp. 460-477
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We use the renormalization group method to study the stochastic Navier–Stokes equation with a random force correlator of the form $k^{4-d-2\varepsilon}$ in a $d$-dimensional space in connection with the problem of constructing a $1/d$-expansion and going beyond the framework of the standard $\varepsilon$-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, $\beta$-function, fixed-point coordinates, and ultraviolet correction index $\omega$) up to the order $\varepsilon^3$ (three-loop approximation). We use the obtained results to propose hypothetical exact expressions (i.e., not in the form of $\varepsilon$-expansions) for the fixed-point coordinate and the index $\omega$.
Keywords: renormalization group, fully developed turbulence. 
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     author = {L. Ts. Adzhemyan and N. V. Antonov and P. B. Goldin and T. L. Kim and M. V. Kompaniets},
     title = {Renormalization group in the~theory of turbulence: {Three-loop} approximation as $d\to\infty$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {460--477},
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     volume = {158},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_158_3_a10/}
}
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L. Ts. Adzhemyan; N. V. Antonov; P. B. Goldin; T. L. Kim; M. V. Kompaniets. Renormalization group in the theory of turbulence: Three-loop approximation as $d\to\infty$. Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 3, pp. 460-477. http://geodesic.mathdoc.fr/item/TMF_2009_158_3_a10/

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