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

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-ξ}. Effects of compressibility of the fluid are studied. It is shown that, depending on the relation between the exponent ξand 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, ξand 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-ξplane, 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.

arXiv comment25 pages, 4 figures

References in corpus (12)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Particles and fields in fluid turbulence
• Universality classes in nonequilibrium lattice systems
• The Field Theory Approach to Percolation Processes
• Levy-flight spreading of epidemic processes leading to percolating clusters
• Anomalous scaling regimes of a passive scalar advected by the synthetic velocity field
• Anomalous scaling of a passive scalar advected by the synthetic compressible flow
• Effects of mixing and stirring on the critical behavior
• Effects of turbulent mixing on the nonequilibrium critical behaviour
• Critical behaviour of a fluid in a random shear flow: Renormalization group analysis of a simplified model
• Field theory of directed percolation with long-range spreading
• Effects of Turbulent Mixing on the Critical Behavior

Cited by in corpus (14)

• Random interface growth in random environment: Renormalization group analysis of a simple model
• Scaling in erosion of landscapes: Renormalization group analysis of a model with turbulent mixing
• The Kardar-Parisi-Zhang model of a random kinetic growth: effects of a randomly moving medium
• Field-theoretic technique for irreversible reaction processes
• Directed percolation process in the presence of velocity fluctuations: Effect of compressibility and finite correlation time
• Renormalization group analysis of a self-organized critical system: Intrinsic anisotropy vs random environment
• Field Theory Approach In Kinetic Reaction: Role Of Random Sources And Sinks
• Critical Behavior of Percolation Process Influenced by Random Velocity Field: One-Loop Approximation
• Critical behaviour of the randomly stirred dynamical Potts model: Novel universality class and effects of compressibility
• Renormalization group study of superfluid phase transition: effect of compressibility
• Influence of turbulent mixing on critical behavior of directed percolation process : effect of compressibility
• Gribov process advected by the synthetic compressible velocity ensemble: Renormalization Group Approach
• Scaling behavior in interacting systems: joint effect of anisotropy and compressibility
• Active-to-absorbing phase transition subjected to the velocity fluctuations in the frozen limit case