Normal and anomalous scaling of the fourthorder correlation function of a randomly advected passive scalar
Abstract
For a δfunctioncorrelated velocity field, simultaneous correlation functions of a passive scalar satisfy closed equations. We analyze the equation for the fourpoint function. To describe a solution completely, one has to solve the matching problems at the scale of the source and at the diffusion scale. We solve both the matching problems and thus find the dependence of the fourpoint correlation function on the diffusion and pumping scale for large space dimensionality d. It is shown that anomalous scaling appears in the first order of 1/d perturbation theory. Anomalous dimensions are found analytically both for the scalar field and for its derivatives, in particular, for the dissipation field.
 Publication:

Physical Review E
 Pub Date:
 November 1995
 DOI:
 10.1103/PhysRevE.52.4924
 arXiv:
 arXiv:chaodyn/9503001
 Bibcode:
 1995PhRvE..52.4924C
 Keywords:

 47.10.+g;
 47.27.i;
 05.40.+j;
 Turbulent flows;
 Nonlinear Sciences  Chaotic Dynamics;
 Condensed Matter;
 High Energy Physics  Theory
 EPrint:
 19 pages, RevTex 3.0, Submitted to Phys.Rev. E, revised version