  The Kardar-Parisi-Zhang model of non-equilibrium critical behaviour (kinetic
surface roughening) with turbulent motion of the environment taken into account
is studied by the field theoretic renormalization group approach. The turbulent
motion is described by the stochastic Navier-Stokes equation with the random
stirring force whose correlation function includes two terms that allow one to
account both for a turbulent fluid and for a fluid in thermal equilibrium. The
renormalization group analysis performed in the leading order of perturbation
theory (one-loop approximation) reveals six possible types of scaling behaviour
(universality classes). The most interesting values of the spatial dimension
$d=2$ and~$3$ correspond to the universality class of a pure turbulent
advection where the nonlinearity of the Kardar--Parisi--Zhang model is
irrelevant.
