Renormalization Group, Operator Product Expansion, and Anomalous Scaling in a Model of Advected Passive Scalar
Abstract
Field theoretical renormalization group methods are applied to the ObukhovKraichnan model of a passive scalar advected by the Gaussian velocity field with the covariance $<{\bf v}(t,{\bf x}){\bf v}(t',{\bf x})>  < v(t,{\bf x}){\bf v}(t',x')> \propto\delta(tt') xx'^{\eps}$. Inertial range anomalous scaling for the structure functions and various pair correlators is established as a consequence of the existence in the corresponding operator product expansions of ``dangerous'' composite operators [powers of the local dissipation rate], whose negative critical dimensions determine anomalous exponents. The main technical result is the calculation of the anomalous exponents in the order $\eps^{2}$ of the $\eps$ expansion. Generalization of the results obtained to the case of a ``slow'' velocity field is also presented.
 Publication:

arXiv eprints
 Pub Date:
 January 1998
 DOI:
 10.48550/arXiv.chaodyn/9801033
 arXiv:
 arXiv:chaodyn/9801033
 Bibcode:
 1998chao.dyn..1033A
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics;
 Condensed Matter
 EPrint:
 Minor grammatical changes, misprints corrected, new references added