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The Kardar-Parisi-Zhang model of non-equilibrium critical behaviour (kineticsurface roughening) with turbulent motion of the environment taken into accountis studied by the field theoretic renormalization group approach. The turbulentmotion is described by the stochastic Navier-Stokes equation with the randomstirring force whose correlation function includes two terms that allow one toaccount both for a turbulent fluid and for a fluid in thermal equilibrium. Therenormalization group analysis performed in the leading order of perturbationtheory (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 turbulentadvection where the nonlinearity of the Kardar--Parisi--Zhang model isirrelevant.

Effects of turbulent environment on the surface roughening: The Kardar-Parisi-Zhang model coupled to the stochastic Navier-Stokes equation