Eur. Phys. J. B 59, 509-518 (2007)
https://doi.org/10.1140/epjb/e2007-00307-0

Transition to chaos via the quasi-periodicity and characterization of attractors in confined Bénard-Marangoni convection

¹ Department of Mechanical Engineering, University of Batna, Rue Boukhlouf Mohamed el Hadi, 05000 Batna, Algeria
² IUSTI - CNRS UMR 6595, Polytech'Marseille, Technopôle de Château-Gombert, 5 rue Enrico Fermi, 13453, Marseille, France

Corresponding authors: ^a samir.rahal@lycos.com - ^b Pierre.Cerisier@polytech.univ-mrs.fr - ^c cherifa.abid@polytech.univ-mrs.fr

Received: 19 February 2007
Revised: 25 September 2007
Published online: 15 November 2007

Abstract

A study of dynamic regimes in Bénard-Marangoni convection was carried out for various Prandtl and Marangoni numbers in small aspect ratio geometries (Γ = 2.2 and 2.8). Experiments in a small hexagonal vessel, for a large range of the Marangoni number (from 148 to 3636), were carried out. Fourier spectra and an auto-correlation function were used to recognize the various dynamic regimes. For given values of the Prandtl number (Pr = 440) and aspect ratio (Γ = 2.2), mono-periodic, bi-periodic and chaotic states were successively observed as the Marangoni number was increased. The correlation dimensions of strange attractors corresponding to the chaotic regimes were calculated. The dimensions were found to be larger than those obtained by other authors for Rayleigh-Bénard convection in aspect ratio geometries of the same order. The transition from temporal chaos to spatio-temporal chaos was also observed. For Γ = 2.2, when larger values of the Marangoni number were imposed (Ma = 1581 for Pr = 160 and Ma = 740 for Pr = 440), spatial modes were involved through the convective pattern dynamics.