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Quasi-periodicity and chaos in a differentially heated cavity

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Abstract

Convective flows of a small Prandtl number fluid contained in a two-dimensional vertical cavity subject to a lateral thermal gradient are studied numerically. The chosen geometry and the values of the material parameters are relevant to semiconductor crystal growth experiments in the horizontal configuration of the Bridgman method. For increasing Rayleigh numbers we find a transition from a steady flow to periodic solutions through a supercritical Hopf bifurcation that maintains the centro-symmetry of the basic circulation. For a Rayleigh number of about ten times that of the Hopf bifurcation, the periodic solution loses stability in a subcritical Neimark–Sacker bifurcation, which gives rise to a branch of quasiperiodic states. In this branch, several intervals of frequency locking have been identified. Inside the resonance horns the stable limit cycles lose and gain stability via some typical scenarios in the bifurcation of periodic solutions. After a complicated bifurcation diagram of the stable limit cycle of the 1:10 resonance horn, a soft transition to chaos is obtained.

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Authors and Affiliations

  1. Dep. Física Aplicada, Universitat Politècnica de Catalunya, Mòdul B4, Campus Nord, 08034, Barcelona, Spain

    Isabel Mercader & Oriol Batiste

  2. Lab. Física Aplicada, Facultat de Ciències Químiques, Univesitat Rovira i Virgili, 43005, Tarragona, Spain

    Xavier Ruiz

Authors
  1. Isabel Mercader
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  2. Oriol Batiste
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  3. Xavier Ruiz
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Correspondence to Isabel Mercader.

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Communicated by

H.J.S. Fernando

PACS

44.25.+f, 47.20.Ky, 47.52.+j

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Mercader, I., Batiste, O. & Ruiz, X. Quasi-periodicity and chaos in a differentially heated cavity. Theor. Comput. Fluid Dyn. 18, 221–229 (2004). https://doi.org/10.1007/s00162-004-0128-2

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  • DOI: https://doi.org/10.1007/s00162-004-0128-2

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