  Model of a passive scalar field advected by the compressible Gaussian
strongly anisotropic velocity field with the covariance $\propto
\delta(t-t^{\prime})|{\bf x}-{\bf x^{\prime}}|^{2\epsilon}$ is studied by using
the field theoretic renormalization group and the operator product expansion.
The inertial-range stability of the corresponding scaling regime is
established. The anomalous scaling of the single-time structure functions is
studied and the corresponding anomalous exponents are calculated. Their
dependence on the compressibility parameter and anisotropy parameters is
analyzed. It is shown that, as in the isotropic case, the presence of
compressibility leads to the decreasing of the critical dimensions of the
important composite operators, i.e., the anomalous scaling is more pronounced
in the compressible systems. All calculations are done to the first order in
$\epsilon$.
