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Bifurcations from steady to quasi-periodic flows in a laterally heated cavity filled with low Prandtl number fluids

Published online by Cambridge University Press:  21 December 2018

A. Medelfef Open the ORCID record for A. Medelfef [Opens in a new window] ,
D. Henry ,
A. Bouabdallah  and
S. Kaddeche
A. Medelfef*
Affiliation:
Laboratoire de Thermodynamique et Systèmes Energétiques, Faculté de Physique, Université des Sciences et de la Technologie Houari Boumediene – USTHB, BP 32, 16111 Bab Ezzouar, Alger, Algérie Laboratoire de Mécanique des Fluides et d’Acoustique, CNRS/Université de Lyon, Ecole Centrale de Lyon/Université Lyon 1/INSA Lyon – ECL, 36 avenue Guy de Collongue, 69134 Ecully CEDEX, France
D. Henry
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, CNRS/Université de Lyon, Ecole Centrale de Lyon/Université Lyon 1/INSA Lyon – ECL, 36 avenue Guy de Collongue, 69134 Ecully CEDEX, France
A. Bouabdallah
Affiliation:
Laboratoire de Thermodynamique et Systèmes Energétiques, Faculté de Physique, Université des Sciences et de la Technologie Houari Boumediene – USTHB, BP 32, 16111 Bab Ezzouar, Alger, Algérie
S. Kaddeche
Affiliation:
Laboratoire de Recherche Matériaux, Mesures et Applications, Institut National des Sciences Appliquées et de Technologie – INSAT, B.P. 676, 1080 Tunis CEDEX, Tunisie
*
†Email address for correspondence: [email protected]
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Abstract

This study deals with the transition toward quasi-periodicity of buoyant convection generated by a horizontal temperature gradient in a three-dimensional parallelepipedic cavity with dimensions $4\times 2\times 1$ (length $\times$ width $\times$ height). Numerical continuation techniques, coupled with an Arnoldi method, are used to locate the steady and Hopf bifurcation points as well as the different steady and periodic flow branches emerging from them for Prandtl numbers ranging from 0 to 0.025 (liquid metals). Our results highlight the existence of two steady states along with many periodic cycles, all with different symmetries. The bifurcation scenarios consist of complex paths between these different solutions, giving a succession of stable flow states as the Grashof number is increased, from steady to periodic and quasi-periodic. The change of these scenarios with the Prandtl number, in connection with the crossing of bifurcation points, was carefully analysed.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Convection: Convection in cavities Instability: Nonlinear instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 861 , 25 February 2019 , pp. 223 - 252
Copyright
© 2018 Cambridge University Press 

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