Geodesic
Renormalization group in the theory of the two-dimensional turbulence: Instability of the fixed point with respect to weak anisotropy
Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 3, pp. 417-427 
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. Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 3, pp. 417-427. http://geodesic.mathdoc.fr/item/TMF_1997_112_3_a5/
@article{TMF_1997_112_3_a5,
     author = {N. V. Antonov and A. V. Runov},
     title = {Renormalization group in the theory of the two-dimensional turbulence: {Instability} of the fixed point with respect to weak anisotropy},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {417--427},
     year = {1997},
     volume = {112},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_112_3_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Statistical model of the fully developed turbulence in the 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 the description of the two-dimensional turbulence.

[1] L. Ts. Adzhemyan, N. V. Antonov, A. N. Vasilev, UFN, 166:12 (1996), 1257–1284 | DOI

[2] R. Rubinstein, J. M. Barton, Phys. Fluids, 30 (1987), 2987 | DOI | Zbl

[3] T. L. Kim, A. V. Serdyukov, TMF, 105 (1995), 412 | Zbl

[4] L. Ts. Adzhemyan, M. Hnatich, D. Horvath, M. Stehlik, Int. J. Mod. Phys. B, 9 (1995), 3401 | DOI

[5] J. Buša, M. Hnatich, J. Honkonen, D. Horvath, Phys. Rev. E, 55 (1997), 381 | DOI

[6] P. Olla, Int. J. Mod. Phys. B, 8 (1994), 581 | DOI

[7] D. Ronis, Phys. Rev. A, 36 (1987), 3322 | DOI

[8] Dzh. Kollinz, Perenormirovka, Mir, M., 1988 | MR

[9] J. Honkonen, M. Yu. Nalimov, Z. Phys. B, 99 (1996), 297 | DOI

[10] R. Kraichnan, Phys. Fluids, 10 (1967), 1417 | DOI

[11] D. Forster, D. R. Nelson, M. J. Stephen, Phys. Rev. A, 16 (1977), 732 | DOI | MR