Effects of turbulent mixing on critical behaviour in the presence of compressibility: Renormalization group analysis of two models

TL;DR

This study uses renormalization group analysis to explore how turbulent mixing and compressibility influence critical behavior in two models, revealing new regimes where nonlinearity and turbulence are both significant.

Contribution

It introduces a detailed RG analysis of two models under turbulent mixing with compressibility, uncovering a new critical regime with exponents depending on multiple parameters.

Findings

Four types of critical behavior identified depending on parameters.

Compressibility broadens the stability region of the new critical regime.

Turbulent transfer is enhanced by nonlinearities and mixing.

Abstract

Critical behaviour of two systems, subjected to the turbulent mixing, is studied by means of the field theoretic renormalization group. The first system, described by the equilibrium model A, corresponds to relaxational dynamics of a non-conserved order parameter. The second one is the strongly non-equilibrium reaction-diffusion system, known as Gribov process and equivalent to the Reggeon field theory. The turbulent mixing is modelled by the Kazantsev-Kraichnan "rapid-change" ensemble: time-decorrelated Gaussian velocity field with the power-like spectrum k^{-d-\xi}. Effects of compressibility of the fluid are studied. It is shown that, depending on the relation between the exponent \xi and the spatial dimension d, the both systems exhibit four different types of critical behaviour, associated with four possible fixed points of the renormalization group equations. The most interesting point corresponds to a new type of critical behaviour, in which the nonlinearity and turbulent mixing are both relevant, and the critical exponents depend on d, \xi and the degree of compressibility. For the both models, compressibility enhances the role of the nonlinear terms in the dynamical equations: the region in the d-\xi plane, where the new nontrivial regime is stable, is getting much wider as the degree of compressibility increases. In its turn, turbulent transfer becomes more efficient due to combined effects of the mixing and the nonlinear terms.