Wall laws for fluid flows at a boundary with random roughness

The general concern of this paper is the effect of rough boundaries on fluids. We consider a stationary flow, governed by incompressible Navier-Stokes equations, in an infinite domain bounded by two horizontal rough plates. The roughness is modeled by a spatially homogeneous random field, with characteristic size epsilon. A mathematical analysis of the flow for small E is performed. The Navier's wall law is rigorously deduced from this analysis. This substantially extends former results obtained in the case of periodic roughness, notably in [16, 17]. (C) 2007 Wiley Periodicals, Inc.