  In this paper we consider the model of incompressible fluid described by the
stochastic Navier-Stokes equation with finite correlation time of a random
force. Inertial-range asymptotic behavior of fully developed turbulence is
studied by means of the field theoretic renormalization group within the
one-loop approximation. It is corroborated that regardless of the values of
model parameters and initial data, the inertial-range behavior of the model is
described by limiting case of vanishing correlation time. It indicates that the
Galilean symmetry of the model violated by the "colored" random force is
restored in the inertial range. This regime corresponds to the only nontrivial
fixed point of the renormalization group equation. The stability of this point
depends on the relation between the exponents in the energy spectrum ${\cal E}
\propto k^{1-y}$ and the dispersion law $\omega \propto k^{2-\eta}$. The second
analyzed problem is the passive advection of a scalar field by this velocity
ensemble. Correlation functions of the scalar field exhibit anomalous scaling
behavior in the inertial-convective range. We demonstrate that in accordance
with Kolmogorov's hypothesis of the local symmetry restoration, the main
contribution to the operator product expansion is given by the isotropic
operator, while anisotropic terms should be considered only as corrections.
