Boussinesq approximations, and beyond, in a tall thermo-gravitational column

Gérard Labrosse

doi:10.1016/j.crme.2007.08.012

Boussinesq approximation, convection

Boussinesq approximations, and beyond, in a tall thermo-gravitational column
[Approximations de Boussinesq et au delà, en très haute colonne thermo-gravitationnelle]

Gérard Labrosse ^1,^2,³

¹ Université Paris-sud, Limsi-CNRS, bâtiment 508, 91405 Orsay cedex, France
² Mathematics Department, Federal University of Santa Catarina, Florianópolis, Brazil
³ Department of Chemical Engineering, University of Florida 237 ChE, P.O. Box 116005, Gainesville, FL 32611, USA

Comptes Rendus. Mécanique, Joseph Boussinesq, a Scientist of bygone days and present times, Volume 335 (2007) no. 9-10, pp. 628-637.

Résumé
Abstract

Cet article présente les points essentiels d'un traitement non-Boussinesq nécessaire pour une analyse théorique des écoulements de base dans une colonne thermo-gravitationnelle, où le coefficient de Soret $S_{T}$ dépend de la température et de la composition, $S_{T} (T, C)$ . Le résultat principal est que la structure horizontale est contrôlée par la dépendance thermique de $S_{T}$ , alors que la dépendance compositionnelle de $S_{T}$ fixe la structure de la stratification compositionnelle verticale.

This article focuses on the main aspects of the non-Boussinesq treatment that is required for analyzing the simplest flow regimes occurring in a tall thermo-gravitational column, when the Soret coefficient $S_{T}$ is considered as depending upon temperature and composition, $S_{T} (T, C)$ . As a main result, the horizontal dynamics is mainly governed by the Soret thermal sensitivity, and the species vertical separation by its compositional one.

Reçu le : 2006-12-06
Accepté le : 2007-05-25
Publié le : 2007-09-01

DOI : 10.1016/j.crme.2007.08.012

Keywords: Fluid mechanics, Boussinesq approximations, Thermo-gravitational column
Mots-clés : Mécanique des fluides, Approximations de Boussinesq, Colonne thermo-gravitationnelle

Affiliations des auteurs :

Gérard Labrosse ^{1, 2, 3}

¹ Université Paris-sud, Limsi-CNRS, bâtiment 508, 91405 Orsay cedex, France
² Mathematics Department, Federal University of Santa Catarina, Florianópolis, Brazil
³ Department of Chemical Engineering, University of Florida 237 ChE, P.O. Box 116005, Gainesville, FL 32611, USA

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     title = {Boussinesq approximations, and beyond, in a tall thermo-gravitational column},
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Gérard Labrosse. Boussinesq approximations, and beyond, in a tall thermo-gravitational column. Comptes Rendus. Mécanique, Joseph Boussinesq, a Scientist of bygone days and present times, Volume 335 (2007) no. 9-10, pp. 628-637. doi : 10.1016/j.crme.2007.08.012. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.08.012/

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Jean K. Platten; Manuel Marcoux; Abdelkader Mojtabi The Rayleigh–Benard problem in extremely confined geometries with and without the Soret effect, Comptes Rendus. Mécanique, Volume 335 (2007) no. 9-10, p. 638 | DOI:10.1016/j.crme.2007.08.011

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