Eur. Phys. J. Special Topics 224, 217–227 (2015)
https://doi.org/10.1140/epjst/e2015-02354-6

Regular Article

Influence of container shape and size on surface-tension-driven Bénard convection

Aix Marseille Université, CNRS, IUSTI UMR 7343, 13453 Marseille, France

^a e-mail: marc.medale@univ-amu.fr

Received: 29 July 2014
Revised: 16 February 2015
Published online: 8 April 2015

Abstract

The aim of this study is to investigate the influence of the container size and shape on the main fluid flow characteristics of Surface-Tension-Driven Bénard Convection. Computations have been performed for high Prandtl number fluids and realistic boundary conditions in various configurations either at steady state when it exists or unsteady one for Ma_c ≤ Ma ≤ 2.5Ma_c. The threshold value, its associated pattern and secondary bifurcation one are presented for each configuration. For very small aspect ratios, it turns out that the threshold value is determined by the friction coefficient whereas for medium size aspect ratios both size and shape enters the game in a more subtle way. Some containers have been found to induce a quasi-perfect hexagonal pattern in their core region provided they satisfy shape and size compatibility conditions. Otherwise, dynamical regimes may appear even close to the threshold so their peculiar characteristics have been reported and analyzed as they seem to be intrinsic to small aspect ratio configurations.