Critical behaviour of a fluid in a random shear flow: Renormalization group analysis of a simplified model
| dc.creator | Antonov, N. V. | |
| dc.creator | Ignatieva, A. A. | |
| dc.date | 2006-07-02 | |
| dc.date.accessioned | 2026-07-07T10:37:01Z | |
| dc.date.available | 2026-07-07T10:37:01Z | |
| dc.description | Critical behaviour of a fluid, subjected to strongly anisotropic turbulent mixing, is studied by means of the field theoretic renormalization group. As a simplified model, relaxational stochastic dynamics of a non-conserved scalar order parameter, coupled to a random velocity field with prescribed statistics, is considered. The velocity is taken Gaussian, white in time, with correlation function of the form $\propto δ(t-t') /|{\bf k}_{\bot}|^{d+ξ}$, where ${\bf k}_{\bot}$ is the component of the wave vector, perpendicular to the distinguished direction (``direction of the flow''). It is shown that, depending on the relation between the exponent $ξ$ and the space dimensionality $d$, the system exhibits various types of large-scale self-similar behaviour, associated with different infrared attractive fixed points of the renormalization-group equations. Existence of a new, non-equilibrium and strongly anisotropic, type of critical behaviour (universality class) is established, and the corresponding critical dimensions are calculated to the second order of the double expansion in $ξ$ and $ε=4-d$ (two-loop approximation). The most realistic values of the model parameters (for example, $d=3$ and the Kolmogorov exponent $ξ=4/3$) belong to this class. The scaling behaviour appears anisotropic in the sense that the critical dimensions related to the directions parallel and perpendicular to the flow are essentially different. | |
| dc.description | IOPLaTeX file, 26 pages, 4 EPS figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0607019 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0607019 | |
| dc.identifier | J.Phys.A39:13593-13620,2006 | |
| dc.identifier | doi:10.1088/0305-4470/39/44/001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/180244 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Chaotic Dynamics | |
| dc.title | Critical behaviour of a fluid in a random shear flow: Renormalization group analysis of a simplified model | |
| dc.type | text |