RENORMALIZATION-GROUP, OPERATOR PRODUCT EXPANSION, AND ANOMALOUS SCALING IN A MODEL OF ADVECTED PASSIVE SCALAR

Field theoretical renormalization group methods are applied to the Obu khov-Kraichnan model of a passive scalar advected by the Gaussian velo city field with the covariance [v(t,x)v(t',x)] - [v(t,x)v(t',x')] prop ortional to delta(t -t')\x-x'\(epsilon). Inertial range anomalous scal ing for the structure functions and various pair correlators is establ ished as a consequence of the existence in the corresponding operator product expansions of certain essential or ''dangerous'' composite ope rators [powers of the local dissipation rate], whose negative critical dimensions determine anomalous exponents. The main technical result i s the calculation of the anomalous exponents in the order epsilon(2) O f the epsilon expansion. Generalization of the results obtained to the case of a ''slow'' velocity field is also presented.