About Boussinesq's turbulent viscosity hypothesis: historical remarks and a direct evaluation of its validity - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Comptes Rendus Mécanique Année : 2007

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

Résumé

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.
Fichier principal
Vignette du fichier
Schmitt-Boussinesq-final.pdf (565.34 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00264386 , version 1 (17-03-2008)

Identifiants

Citer

François G Schmitt. About Boussinesq's turbulent viscosity hypothesis: historical remarks and a direct evaluation of its validity. Comptes Rendus Mécanique, 2007, 335 (9-10), pp.617-627. ⟨10.1016/j.crme.2007.08.004⟩. ⟨hal-00264386⟩
2669 Consultations
13237 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More