Wall laws for fluid flows at a boundary with random roughness

Details Wall laws for fluid flows at a boundary with random roughness Wall laws for fluid flows at a boundary with random roughness

2006-06-29

arxiv.org/abs/math/0606768v1

Mathematics

Analysis of PDEs

Scientific paper

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 $\eps$. A mathematical analysis of the flow for small $\eps$ is performed. The Navier's wall law is rigorously deduced from this analysis.

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