Effects of turbulent transfer on the critical behaviour

TL;DR

This paper investigates how turbulent mixing influences the critical behavior of two different systems using field theoretic renormalization group methods, revealing new universality classes and calculating critical dimensions.

Contribution

It introduces a novel analysis of turbulent transfer effects on critical phenomena, identifying new universality classes and deriving critical dimensions in a double expansion framework.

Findings

Identification of various critical behaviors depending on y and d

Existence of new strongly nonequilibrium universality classes

Calculation of critical dimensions to first order in y and ε

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 nonequilibrium reaction-diffusion system, known as Gribov process or directed percolation process. The turbulent mixing is modelled by the stochastic Navier-Stokes equation with random stirring force with the correlator \propto \delta(t-t') p^{4-d-y}, where p is the wave number, d is the space dimension and y the arbitrary exponent. It is shown that, depending on the relation between y and d, the systems exhibit various types of critical behaviour. In addition to known regimes (original systems without mixing and passively advected scalar field), existence of new strongly nonequilibrium universality classes is established, and the corresponding critical dimensions are calculated to the first order of the double expansion in y and \epsilon=4-d (one-loop approximation).