RENORMALIZATION-GROUP IN THE THEORY OF DEVELOPED TURBULENCE - THE PROBLEM OF JUSTIFYING THE KOLMOGOROV HYPOTHESES FOR COMPOSITE-OPERATORS

In this paper, the stochastic theory of developed turbulence is consid ered within the framework of the quantum field renormalization group a nd operator expansions. The problem of justifying the Kolmogorov-Obukh ov theorem in application to the correlation functions of composite op erators is discussed. An explicit expression is found for the critical dimension of a general-type composite operator. For an arbitrary UV-f inite composite operator, the second Kolmogorov hypothesis (the viscos ity-independence of the correlator) is proved and the dependence of va rious correlators on the external turbulence scale is determined. It i s shown that the problem involves an infinite number of Galilean-invar iant scalar operators with negative critical dimensions.