Nonuniversality of the Scaling Exponents of a Passive Scalar Convected by a Random Flow
Abstract
We consider a passive scalar convected by a multiscale random velocity field with short yet finite temporal correlations. Taking Kraichnan's limit of a white Gaussian velocity as a zero approximation we develop the perturbation theory with respect to a small correlation time and small nonGaussianity of the velocity. We derive the renormalization (due to temporal correlations and nonGaussianity) of the operator of turbulent diffusion. That allows us to calculate the respective corrections to the anomalous scaling exponents of the scalar field and show that they continuously depend on velocity correlation time and the degree of nonGaussianity. The scalar exponents are thus nonuniversal as was predicted by Shraiman and Siggia on a phenomenological ground.
 Publication:

Physical Review Letters
 Pub Date:
 May 1996
 DOI:
 10.1103/PhysRevLett.76.3707
 arXiv:
 arXiv:chaodyn/9601016
 Bibcode:
 1996PhRvL..76.3707C
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics;
 Condensed Matter;
 High Energy Physics  Theory
 EPrint:
 4 pages, RevTex 3.0, Submitted to Phys.Rev.Lett