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

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, Volume 335 (2007) no. 9-10, pp. 628-637.

Abstract
Résumé

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.

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.

Received: 2006-12-06
Accepted: 2007-05-25
Published online: 2007-09-01

DOI: 10.1016/j.crme.2007.08.012

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

Author's affiliations:

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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     pages = {628--637},
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Gérard Labrosse. Boussinesq approximations, and beyond, in a tall thermo-gravitational column. Comptes Rendus. Mécanique, 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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