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

Renormalization group analysis of a turbulent compressible fluid neard= 4: Crossover between local and non-local scaling regimes

“…This shows us, that the simple analysis around d = 3, which indicates existence of only one nontrivial fixed point [1], is incomplete in this case.…”

“…As it has been shown in [1] and discussed in [14], the model (5) - (6) is invariant with respect to the Galilean symmetry, which results to the UV finitness of the two Green's functions:…”

“…They can be absorbed by a suitable local counterterm v i ∇ 2 v i , and a regular expansion in both y and ε = d − 2 was constructed. Up to now the present model (5) has been investigated at the fixed space dimension d = 3, for which the action (5) contains all terms that can be generated during the renormalization procedure [1,[13][14][15]. However, using the dimensional analysis it can be shown that at d = 4 there appears an additional divergence, also in the Green's function v v .…”

“…1. Explicit expressions of propagators in frequency-momentum representation can be found, e.g., in [1], and they are right for actual calculations. The ultraviolet (UV) renormalizability is very efficiently revealed by an analysis of the 1-irreducible Green's functions.…”

“…However, a similar treatment has been only scarcely applied to compressible fluids. In this paper we present an application of the field theoretic renormalization group (RG) onto the scaling regimes of a compressible fluid, whose behavior is governed by a proper generalization of stochastic Navier Stokes equation [1]. Similar models of compressible fluid were considered in [2][3][4].…”