  We study a model of fully developed turbulence of a compressible fluid, based
on the stochastic Navier-Stokes equation, by means of the field theoretic
renormalization group. In this approach, scaling properties are related to the
fixed points of the renormalization group equations. Previous analysis of this
model near the real-world space dimension 3 identified some scaling regime
[Theor. Math. Phys., 110, 3 (1997)]. The aim of the present paper is to explore
the existence of additional regimes, that could not be found using the direct
perturbative approach of the previous work, and to analyze the crossover
between different regimes. It seems possible to determine them near the special
value of space dimension $4$ in the framework of double $y$ and $\varepsilon$
expansion, where $y$ is the exponent associated with the random force and
$\varepsilon=4-d$ is the deviation from the space dimension $4$. Our
calculations show that there exists an additional fixed point that governs
scaling behavior. Turbulent advection of a passive scalar (density) field by
this velocity ensemble is considered as well. We demonstrate that various
correlation functions of the scalar field exhibit anomalous scaling behavior in
the inertial-convective range. The corresponding anomalous exponents,
identified as scaling dimensions of certain composite fields, can be
systematically calculated as a series in $y$ and $\varepsilon$. All
calculations are performed in the leading one-loop approximation.
