Physics – Condensed Matter
Scientific paper
1998-01-27
Phys. Rev. E 58 (1998): 1823
Physics
Condensed Matter
Minor grammatical changes, misprints corrected, new references added; results and formulas unchanged
Scientific paper
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.
Adzhemyan Loran Ts.
Antonov Nikolaj V.
Vasil'ev Alexander N.
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