  Motivated by the ubiquity of turbulent flows in realistic conditions, effects
of turbulent advection on two models of classical non-linear systems are
investigated. In particular, we analyze model A (according to the
Hohenberg-Halperin classification [1]) of a non-conserved order parameter and a
model of the direct bond percolation process. Having two paradigmatic
representatives of distinct stochastic dynamics, our aim is to elucidate to
what extent velocity fluctuations affect their scaling behavior. The main
emphasis is put on an interplay between anisotropy and compressibility of the
velocity flow on their respective scaling regimes. Velocity fluctuations are
generated by means of the Kraichnan rapid-change model, in which the anisotropy
is due to a distinguished spatial direction n and a correlator of the velocity
field obeys the Gaussian distribution law with prescribed statistical
properties. As the main theoretical tool, the field-theoretic perturbative
renormalization group is adopted. Actual calculations are performed in the
leading (one-loop) approximation. Having obtained infra-red stable asymptotic
regimes, we have found four possible candidates for macroscopically observable
behavior for each model. In contrast to the isotropic case, anisotropy brings
about enhancement of non-linearities and non-trivial regimes are proved to be
more stable.
