Composite operators, short–distance expansion and Galilean invariance in the theory of fully developed turbulence. Infrared corrections to the Kolmogorov's scaling

The infrared asymtotic of the velocity correlator in the theory of developed turbulence is studied by the quantum–field renormalization group and the operator expansion. The scaling dimensionalities of all composite operators constructed from the velocity field and its time derivatives are calculated, the contribution of these operators to the short–distance expansion are determined. It is shown that the asymptotics of the equal–time correlator is determined by the Galilean invariant composite operators. The corrections to the Kolmogorov's spectrum connected with the operators of canonical dimensionality $d=6$ are calculated. The consequences of Galilean invariance for the renormalization of composite operators are considered.