Prog. Theor. Phys. Vol. 52 No. 5 (1974) pp. 1438-1447
Vertex Correction in Turbulence
Department of Physics, Chuo University, Kasuga, Bunkyo-ku, Tokyo
(Received December 25, 1973)
Vertex corrections due to small-scale fluctuations in homogeneous, isotropic turbulence of incompressible fluids are considered. Starting with Kolmogorov's results, the vertex function is calculated in the framework of the summation of all the first-order irreducible diagrams; it is shown to be scaled in the same way as the bare vertex function. Based on general arguments about higher-order diagrams, however, the possibility of logarithmic or even stronger corrections for the fully-renormalized vertex is suggested. If these corrections play a major role, the energy spectrum may have the additional logarithmic or power-law dependence apart from k-5/3.
DOI : 10.1143/PTP.52.1438
T. Nakano, Ann. of Phys. 73 (1972), 326[CrossRef].
- A. N. Kolmogorov, Compt. Rend. Acad. Sci. USSR 30 (1941), 301 [Sov. Phys. -Uspekhi 10 (1968), 734].
- A. V. Shut'ko, Dokl. Akad. Nauk SSSR 158 (1964), 1058 [Sov. Phys. -Doklady 9 (1965), 857].
H. W. Wyld, Jr., Ann. of Phys. 14 (1961), 143[CrossRef].
A. M. Obukhov, J. Fluid Mech. 13 (1962), 77[CrossRef].
A. N. Kolmogorov, J. Fluid Mech. 13 (1962), 82[CrossRef].
A. S. Gurvich and A. M. Yaglom, Phys. Fluids Suppl. (1967), S59.
R. H. Kraichnan, Phys. Rev. Lett. 31 (1973), 744[APS].
See also M. Nelkin, Phys. Rev. A 9 (1974), 388, [APS]in which the analogy between turbulence and phase transition is discussed.
Citing Article(s) :
Progress of Theoretical Physics Vol. 65 No. 1 (1981) pp. 120-139
Effects of Large-Scale Fluctuations in Fully Developed Turbulence
Tohru Nakano and Fumihiko Tanaka