Stochastic Navier-Stokes equation for a compressible fluid: two-loop approximation

A model of fully developed turbulence of a compressible fluid is briefly reviewed. It is assumed that fluid dynamics is governed by a stochastic version of Navier-Stokes equation. We show how corresponding field theoretic-model can be obtained and further analyzed by means of the perturbative renormalization group. Two fixed points of the RG equations are found. The perturbation theory is constructed within formal expansion scheme in parameter $y$, which describes scaling behavior of random force fluctuations. Actual calculations for fixed points' coordinates are performed to two-loop order.