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 Obukhov--Kraichnan model of a passive scalar advected by the Gaussian velocity field with the covariance $<{\bf v}(t,{\bf x}){\bf v}(t',{\bf x})> - < v(t,{\bf x}){\bf v}(t',x')> \propto\delta(t-t')| x-x'|^{\eps}$. 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:
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arXiv e-prints
- Pub Date:
- January 1998
- DOI:
- 10.48550/arXiv.chao-dyn/9801033
- arXiv:
- arXiv:chao-dyn/9801033
- Bibcode:
- 1998chao.dyn..1033A
- Keywords:
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- Nonlinear Sciences - Chaotic Dynamics;
- Condensed Matter
- E-Print:
- Minor grammatical changes, misprints corrected, new references added