Title :

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

Author(s) :

Schmitt, François G [Auteur]
Laboratoire d’Océanologie et de Géosciences (LOG) - UMR 8187 [LOG]
Ecosystèmes Littoraux et Cotiers

Journal title :

Comptes Rendus Mécanique

Pages :

617-627

Publisher :

Elsevier

Publication date :

2007-10

Keyword(s) :

Fluid Mechanics
Turbulence
Constitutive equation

HAL domain(s) :

Physique [physics]/Physique [physics]/Analyse de données, Statistiques et Probabilités [physics.data-an]
Physique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph]
Sciences de l'ingénieur [physics]/Mécanique [physics.med-ph]/Mécanique des fluides [physics.class-ph]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

• Laboratoire d'Océanologie et de Géosciences (LOG) - UMR 8187

Source :

Harvested from HAL