  Field theoretical renormalization group methods are applied to a simple model
of a passive scalar quantity advected by the Gaussian non-solenoidal
(``compressible'') velocity field with the covariance $\propto\delta(t-t')|
x-x'|^{\epsilon}$. Convective range anomalous scaling for the structure
functions and various pair correlators is established, and the corresponding
anomalous exponents are calculated to the order $\epsilon^2$ of the $\epsilon$
expansion. These exponents are non-universal, as a result of the degeneracy of
the RG fixed point. In contrast to the case of a purely solenoidal velocity
field (Obukhov--Kraichnan model), the correlation functions in the case at hand
exhibit nontrivial dependence on both the IR and UV characteristic scales, and
the anomalous scaling appears already at the level of the pair correlator. The
powers of the scalar field without derivatives, whose critical dimensions
determine the anomalous exponents, exhibit multifractal behaviour. The exact
solution for the pair correlator is obtained; it is in agreement with the
result obtained within the $\epsilon$ expansion. The anomalous exponents for
passively advected magnetic fields are also presented in the first order of the
$\epsilon$ expansion.
