The Navier wall law at a boundary with random roughness
نویسنده
چکیده
We consider the Navier-Stokes equation in a domain with irregular boundaries. The irregularity is modeled by a spatially homogeneous random process, with typical size ε≪ 1. In the parent paper [8], we derived a homogenized boundary condition of Navier type as ε→ 0. We show here that for a large class of boundaries, this Navier condition provides a O(ε3/2| ln ε|1/2) approximation in L, instead of O(ε) for periodic irregularities. Our result relies on the study of an auxiliary boundary layer system. Decay properties of this boundary layer are deduced from a central limit theorem for dependent variables.
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