HAL : hal-00264386, version 1

DOI : 10.1016/j.crme.2007.08.004

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Comptes Rendus Mecanique 335, 9-10 (2007) 617-627

About Boussinesq's turbulent viscosity hypothesis: historical remarks and a direct evaluation of its validity

Francois Schmitt 1, 2

(10/2007)

Boussinesq's hypothesis is at the heart of eddy viscosity models, which are used in many different fields to model turbulent flows. In its present time formulation, this hypothesis corresponds to an alignment between Reynolds stress and mean strain tensors. We begin with historical remarks on Boussinesq's results and recall that he introduced a local averaging twenty years before Reynolds, but using an approach that prevented him from discovering Reynolds' stress tensor. We then introduce an indicator that characterizes the validity of this hypothesis. For experimental and numerical databases, when the tensors are known, this can be used to directly estimate the validity of this hypothesis. We show, using several different databases, that this hypothesis is almost never verified. We address in conclusion the analogy with kinetic theory, and the reason why this analogy cannot be applied in general for turbulent flows.

1 :	Ecosystèmes Littoraux et Cotiers
	CNRS : FRE2816 – Université Lille I - Sciences et technologies
2 :	Laboratoire d'Océanologie et de Géosciences (LOG)
	CNRS : UMR8187 – Université Lille I - Sciences et technologies – Université du Littoral Côte d'Opale

Domaine

:

Physique/Physique/Analyse de données, Statistiques et Probabilités Physique/Mécanique/Mécanique des fluides Sciences de l'ingénieur/Mécanique/Mécanique des fluides

Mots Clés : Fluid Mechanics – Turbulence – Constitutive equation

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Contributeur : Francois Schmitt <>

Soumis le : Lundi 17 Mars 2008, 13:33:20

Dernière modification le : Lundi 17 Mars 2008, 14:17:54