  Critical behaviour of a fluid, subjected to strongly anisotropic turbulent
mixing, is studied by means of the field theoretic renormalization group. As a
simplified model, relaxational stochastic dynamics of a non-conserved scalar
order parameter, coupled to a random velocity field with prescribed statistics,
is considered. The velocity is taken Gaussian, white in time, with correlation
function of the form $\propto \delta(t-t') /|{\bf k}_{\bot}|^{d+\xi}$, where
${\bf k}_{\bot}$ is the component of the wave vector, perpendicular to the
distinguished direction (``direction of the flow''). It is shown that,
depending on the relation between the exponent $\xi$ and the space
dimensionality $d$, the system exhibits various types of large-scale
self-similar behaviour, associated with different infrared attractive fixed
points of the renormalization-group equations. Existence of a new,
non-equilibrium and strongly anisotropic, type of critical behaviour
(universality class) is established, and the corresponding critical dimensions
are calculated to the second order of the double expansion in $\xi$ and
$\epsilon=4-d$ (two-loop approximation). The most realistic values of the model
parameters (for example, $d=3$ and the Kolmogorov exponent $\xi=4/3$) belong to
this class. The scaling behaviour appears anisotropic in the sense that the
critical dimensions related to the directions parallel and perpendicular to the
flow are essentially different.
