  The field theoretic renormalization group and operator product expansion are
applied to the problem of a passive scalar advected by the Gaussian
nonsolenoidal velocity field with finite correlation time, in the presence of
large-scale anisotropy. The energy spectrum of the velocity in the inertial
range has the form $E(k)\propto k^{1-\epsilon}$, and the correlation time at
the wavenumber $k$ scales as $k^{-2+\eta}$. It is shown that, depending on the
values of the exponents $\epsilon$ and $\eta$, the model exhibits various types
of inertial-range scaling regimes with nontrivial anomalous exponents. Explicit
asymptotic expressions for the structure functions and other correlation
functions are obtained; they are represented by superpositions of power laws
with nonuniversal amplitudes and universal (independent of the anisotropy)
anomalous exponents, calculated to the first order in $\epsilon$ and $\eta$ in
any space dimension. These anomalous exponents are determined by the critical
dimensions of tensor composite operators built of the scalar gradients, and
exhibit a kind of hierarchy related to the degree of anisotropy: the less is
the rank, the less is the dimension and, consequently, the more important is
the contribution to the inertial-range behavior. The leading terms of the even
(odd) structure functions are given by the scalar (vector) operators. The
anomalous exponents depend explicitly on the degree of compressibility.
