  Critical behaviour of two systems, subjected to the turbulent mixing, is
studied by means of the field theoretic renormalization group. The first
system, described by the equilibrium model A, corresponds to relaxational
dynamics of a non-conserved order parameter. The second one is the strongly
non-equilibrium reaction-diffusion system, known as Gribov process and
equivalent to the Reggeon field theory. The turbulent mixing is modelled by the
Kazantsev-Kraichnan "rapid-change" ensemble: time-decorrelated Gaussian
velocity field with the power-like spectrum k^{-d-\xi}. Effects of
compressibility of the fluid are studied. It is shown that, depending on the
relation between the exponent \xi and the spatial dimension d, the both systems
exhibit four different types of critical behaviour, associated with four
possible fixed points of the renormalization group equations. The most
interesting point corresponds to a new type of critical behaviour, in which the
nonlinearity and turbulent mixing are both relevant, and the critical exponents
depend on d, \xi and the degree of compressibility. For the both models,
compressibility enhances the role of the nonlinear terms in the dynamical
equations: the region in the d-\xi plane, where the new nontrivial regime is
stable, is getting much wider as the degree of compressibility increases. In
its turn, turbulent transfer becomes more efficient due to combined effects of
the mixing and the nonlinear terms.
