Diagram equations of the theory of fully developed turbulence
Teoretičeskaâ i matematičeskaâ fizika, Tome 101 (1994) no. 1, pp. 28-37 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Skeleton diagram equations of turbulence theory – the Dyson equations and the equations for vertices of three types – are obtained nonperturbatively. Their derivation is based on the use of an equation in functional derivatives for the characteristic functional of a hydrodynamic system described by Navier–Stokes equations in the presence of an external random force. The iterative solution of these equations reproduces the perturbation series for second moments that is usually obtained in a more complicated way and also the series for the third moments.
@article{TMF_1994_101_1_a1,
     author = {\'E. V. Teodorovich},
     title = {Diagram equations of the theory of fully developed turbulence},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {28--37},
     year = {1994},
     volume = {101},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_101_1_a1/}
}
TY  - JOUR
AU  - É. V. Teodorovich
TI  - Diagram equations of the theory of fully developed turbulence
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1994
SP  - 28
EP  - 37
VL  - 101
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1994_101_1_a1/
LA  - ru
ID  - TMF_1994_101_1_a1
ER  - 
%0 Journal Article
%A É. V. Teodorovich
%T Diagram equations of the theory of fully developed turbulence
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1994
%P 28-37
%V 101
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1994_101_1_a1/
%G ru
%F TMF_1994_101_1_a1
É. V. Teodorovich. Diagram equations of the theory of fully developed turbulence. Teoretičeskaâ i matematičeskaâ fizika, Tome 101 (1994) no. 1, pp. 28-37. http://geodesic.mathdoc.fr/item/TMF_1994_101_1_a1/

[1] Wyld H. W., Ann. Phys., 14:6 (1961), 143–165 | DOI | MR | Zbl

[2] Lee L. L., Ann. Phys., 32:2 (1965), 292–321 | DOI | Zbl

[3] Monin A. C., Yaglom A. M., Statisticheskaya gidromekhanika, t. 2, Nauka, M., 1967

[4] Gledzer E. B., Monin A. S., UMN, 29:3 (1974), 111–159 | MR | Zbl

[5] Zakharov V. E., Lvov B. C., Izv. vuzov. Radiofizika, 28:10 (1975), 1470–1487

[6] Lvov V. S., Lektsii po volnovoi i gidrodinamicheskoi turbulentnosti, NGU, Novosibirsk, 1978

[7] Kraichnan R. H., J. Fluid Mech., 5:4 (1959), 497–543 | DOI | MR | Zbl

[8] Chandrasekhar S., Proc. Roy. Soc. A, 229:1176 (1959), 1–19 | DOI | MR

[9] Shutko A. V., DAN SSSR, 158:5 (1964), 1058–1060 | MR

[10] Martin P. C., Siggia E. D., Rose H. A., Phys. Rev. A, 8:1 (1973), 423–437 | DOI

[11] Teodorovich E. V., Uspekhi mekhaniki, 13:1 (1990), 81–121 | MR

[12] Adzhemyan L. Ts., Vasilev A. N., Pismak Yu. M., TMF, 57:2 (1983), 268–281 | MR | Zbl

[13] Teodorovich E. V., PMM, 53:3 (1989), 443–447 | MR | Zbl

[14] Kraichnan R. H., Proc. Symp. Dynamics of Fluids and Plasmas, Acad. Press, N. Y., 1966, 239–255

[15] L'vov V. S., Lebedev V. V., Phys. Rev. E, 47:3 (1993), 1794–1803 | DOI | MR