Renormalization group in the problem of the fully developed turbulence of a compresible fluid

A model of the fully developed turbulence of a compressible fluid based on the stohastic Navier–Stokes equation is considered by means of the field theoretic renormalization group. It is proved that the model is multiplicatively renormalizable in terms of the variables “velocity – logarithm of the pressure”. The scaling dimensions of the fields and parameters are calculated in the first order of the $\epsilon$-expansion. The dependence of the effective sound velocity and the Mach number on the integral turbulence scale $L$ is studied.