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

Abstract

We study scaling properties of the model of fully developed turbulence for a compressible fluid, based on the stochastic Navier-Stokes equation, by means of the field theoretic renormalization group (RG). The scaling properties in this approach are related to fixed points of the RG equation. Here we study a possible existence of other scaling regimes and an opportunity of a crossover between them. This may take place in some other space dimensions, particularly at $d=4$. A new regime may there arise and then by continuity moves into $d=3$. Our calculations have shown that there really exists an additional fixed point, that may govern scaling behaviour.

6 pages. arXiv admin note: substantial text overlap with arXiv:1611.00327

References in corpus (2)

• An improved $\eps$ expansion for three-dimensional turbulence: two-loop renormalization near two dimensions
• Anomalous scaling of passive scalar fields advected by the Navier-Stokes velocity ensemble: Effects of strong compressibility and large-scale anisotropy

Cited by in corpus (2)

• Advection of a passive scalar field by turbulent compressible fluid: renormalization group analysis near $d=4$
• Stochastic Navier-Stokes equation and advection of a tracer field: One-loop renormalization near $d=4$