  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
nonequilibrium reaction-diffusion system, known as Gribov process or directed
percolation process. The turbulent mixing is modelled by the stochastic
Navier-Stokes equation with random stirring force with the correlator \propto
\delta(t-t') p^{4-d-y}, where p is the wave number, d is the space dimension
and y the arbitrary exponent. It is shown that, depending on the relation
between y and d, the systems exhibit various types of critical behaviour. In
addition to known regimes (original systems without mixing and passively
advected scalar field), existence of new strongly nonequilibrium universality
classes is established, and the corresponding critical dimensions are
calculated to the first order of the double expansion in y and \epsilon=4-d
(one-loop approximation).

Statistical Mechanics;Chaotic Dynamics