Composite operators,operator expansion,and Galilean invariance in the theory of fully developed turbulence. Infrared corrections to Kolmogorov scaling

The quantum-field renormalization group and operator expansion are used to investigate the infrared asymptotic behavior of the velocity correlation function in the theory of fully developed turbulence. The scaling dimensions of all composite operators constructed from the velocity field and its time derivatives are calculated, and their contributions to the operator expansion are determined. It is shown that the asymptotic behavior of the equal-time correlation function is determined by Galilean-invariant composite operators. The corrections to the Kolmogorov spectrum associated with the operators of canonical dimension 6 are found. The consequences of Galilean invariance for the renormalized composite operators are considered.State University, St. Petersburg. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 100, No. 3, pp. 382–401, September, 1994.