Wall laws for viscous fluids near rough surfaces

Bucur, Dorin, Dalibard, Anne-Laure, and Gérard-Varet, David. Cancès, E., and Labbé, S., eds. " Wall laws for viscous fluids near rough surfaces ." ESAIM: Proceedings 37 (2012): 117-135. <http://eudml.org/doc/251276>.

@article{Bucur2012,
abstract = {In this paper, we review recent results on wall laws for viscous fluids near rough surfaces, of small amplitude and wavelength ε. When the surface is “genuinely rough”, the wall law at first order is the Dirichlet wall law: the fluid satisfies a “no-slip” boundary condition on the homogenized surface. We compare the various mathematical characterizations of genuine roughness, and the corresponding homogenization results. At the next order, under ergodicity properties of the roughness distribution, a Navier wall law with a slip length of order ε can be derived, that leads to better error estimates. We also discuss the relationship beween the slip length and the position of the homogenized surface. In particular, we prove that for adherent rough walls, the Navier wall law associated to the roughness does not correspond to any tangible slip.},
author = {Bucur, Dorin, Dalibard, Anne-Laure, Gérard-Varet, David},
editor = {Cancès, E., Labbé, S.},
journal = {ESAIM: Proceedings},
language = {eng},
month = {9},
pages = {117-135},
publisher = {EDP Sciences},
title = { Wall laws for viscous fluids near rough surfaces },
url = {http://eudml.org/doc/251276},
volume = {37},
year = {2012},
}

TY - JOUR
AU - Bucur, Dorin
AU - Dalibard, Anne-Laure
AU - Gérard-Varet, David
AU - Cancès, E.
AU - Labbé, S.
TI - Wall laws for viscous fluids near rough surfaces
JO - ESAIM: Proceedings
DA - 2012/9//
PB - EDP Sciences
VL - 37
SP - 117
EP - 135
AB - In this paper, we review recent results on wall laws for viscous fluids near rough surfaces, of small amplitude and wavelength ε. When the surface is “genuinely rough”, the wall law at first order is the Dirichlet wall law: the fluid satisfies a “no-slip” boundary condition on the homogenized surface. We compare the various mathematical characterizations of genuine roughness, and the corresponding homogenization results. At the next order, under ergodicity properties of the roughness distribution, a Navier wall law with a slip length of order ε can be derived, that leads to better error estimates. We also discuss the relationship beween the slip length and the position of the homogenized surface. In particular, we prove that for adherent rough walls, the Navier wall law associated to the roughness does not correspond to any tangible slip.
LA - eng
UR - http://eudml.org/doc/251276
ER -