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Wall laws for fluid flows at a boundary with random roughness

Arnaud Basson·David Gerard-Varet
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Abstract

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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Arnaud Basson, David Gerard-Varet. 2006-06-29. Wall laws for fluid flows at a boundary with random roughness. https://arxiv.org/abs/math/0606768

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