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

Abstract

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.

10 pages, 1 figure

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• Stirred Kardar-Parisi-Zhang equation with quenched random noise: Emergence of induced nonlinearity
• The BLUES function method applied to partial differential equations and analytic approximants for interface growth under shear
• Field Theoretic Renormalization Group in an Infinite-Dimensional Model of Random Surface Growth in Random Environment
• Effect of random environment on kinetic roughening: Kardar-Parisi-Zhang model with a static noise coupled to the Navier-Stokes equation
• Renormalization group analysis of a continuous model with self-organized criticality: Effects of randomly moving environment