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The renormalization group and operator product expansion are applied to themodel of a passive scalar quantity advected by the Gaussian self-similarvelocity field with finite, and not small, correlation time. The inertial-rangeenergy spectrum of the velocity is chosen in the form $E(k)\proptok^{1-2\eps}$, and the correlation time at the wavenumber $k$ scales as$k^{-2+\eta}$. Inertial-range anomalous scaling for the structure functions andother correlation functions emerges as a consequence of the existence in themodel of composite operators with negative scaling dimensions, identified withanomalous exponents. For $\eta>\eps$, these exponents are the same as in therapid-change limit of the model; for $\eta<\eps$, they are the same as in thelimit of a time-independent (quenched) velocity field. For $\eps=\eta$ (localturnover exponent), the anomalous exponents are nonuniversal through thedependence on a dimensionless parameter, the ratio of the velocity correlationtime and the scalar turnover time. The universality reveals itself, however,only in the second order of the $\eps$ expansion, and the exponents are derivedto order $O(\eps^{2})$, including anisotropic contributions. It is shown that,for moderate $n$, the order of the structure function, and $d$, the spacedimensionality, finite correlation time enhances the intermittency incomparison with the both limits: the rapid-change and quenched ones. Thesituation changes when $n$ and/or $d$ become large enough: the correction tothe rapid-change limit due to the finite correlation time is positive (that is,the anomalous scaling is suppressed), it is maximal for the quenched limit andmonotonically decreases as the correlation time tends to zero.Comment: 12 pages, 3 figure

Anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time: Two-loop approximation