Renormalization group approach and short-distance expansion in theory of developed turbulence: Asymptotics of the triplex equal-time correlation function

Asymptotics of the equal time triplex correlation function for the developed turbulence of the incompressible fluid in the region of the strongly separated values of the wave vectors by the renormalization group approach and short distance expansion has been investigated. The problem of the most essential composite operator, giving contribution in this asymptotics, has been examined. For this purpose the critical dimension of the family of the tensor composite operators, which are square on the velocity gradient, have been found. The contribution of such operators in tested one-loop approximation turns out to be less essential (although insignificantly), than contribution of the linear term. The obtained asymptotics of the triplex correlator coincides by the form with one predicted by the EDQNM-approximation.