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

Abstract

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.

Stochastic Navier-Stokes equation and advection of a tracer field: One-loop renormalization neard= 4

“…The term proportional to g 20 is not dictated by the physics of the fluid, but rather by a proper renormalization treatment [39]. In [37] three IR attractive fixed points, which defines possible scaling regimes of the system, were discussed. The character of the IR behaviour depends on the mutual relation between y and ε -two formally small quantities which were introduced in the correlator of the random force in the NavierStokes equation.…”

“…In [37] the critical dimension of the passive scalar density field θ and the field θ ′ were obtained for the fixed points FPII and FPIII:…”

“…The expressions for the propagators and vertices at the bottom of the diagram can be found in [37,39]. Then using the chain rule and up to irrelevant terms the vertex (18) for the operator F (n,l) can be presented in the form Give the exact title of the conference The differentiation yields…”

“…The paper is a logical continuation of our previous studies [37,38] and is organized as follows. In the introductory Section 2 a brief discussion of the fixed points' structure and possible scaling regimes is presented.…”

Passive Advection of a Vector Field by Compressible Turbulent Flow: Renormalizations Group Analysis near d = 4

“…This paper is a continuation of our previous works [42][43][44][45] and is organized as follows. In the introductory Section 2 we give a brief overview of the model.…”