Kinetic Roughening in Turbulent Environment: Spatially Quenched Kardar–Parisi–Zhang Model and Navier–Stokes Equation

Using field-theoretic renormalization group analysis, we study the Kardar–Parisi–Zhang equation of random surface growth with a spatially quenched random noise taking into account turbulent environment described by the Navier–Stokes equation. The latter is taken in the form that allows to model both macroscopic shaking of the fluid and fully turbulent flow. After establishing multiplicative renormalizability of the constructed action functional with additional non-linearity, we perform one-loop calculations (to the leading order in $$\varepsilon = 4 - d$$ and $$y$$ where $$d$$ is the space dimension) and find three sets of renormalization group equations’ fixed points: Gaussian fixed point (regime of ordinary diffusion), a curve of fixed points (macroscopic shaking) with infrared attractive segment, and a surface of fixed points for a special case $$\varepsilon = y$$ that also involved infrared attractive area. We also investigate marginal values of the coupling constants to look for “hidden” fixed points.