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Wall laws for fluid flows at a boundary with random roughness
Author(s) -
Basson Arnaud,
GérardVaret David
Publication year - 2008
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20237
Subject(s) - mathematics , bounded function , surface finish , compressibility , domain (mathematical analysis) , flow (mathematics) , boundary (topology) , homogeneous , mathematical analysis , navier–stokes equations , vector field , incompressible flow , field (mathematics) , geometry , mechanics , physics , materials science , pure mathematics , combinatorics , composite material
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 ε. A mathematical analysis of the flow for small ε 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]. © 2007 Wiley Periodicals, Inc.