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Complex transition to chaotic flow in a periodic array of cylinders

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Abstract

This paper presents a numerical study of the transition to chaos of the flow of a Newtonian fluid in a periodic array of cylinders between two parallel walls. Using tools from dynamical system theory, we identify and characterize the different solutions to the Navier-Stokes equations at different values of the Reynolds number. We show that a very complex transition to chaos occurs for this problem where we first observe two incommensurate frequencies and then a frequency locking followed by a few period doublings following Feigenbaum's route to turbulence.

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Authors and Affiliations

  1. Départment de Mathématiques Appliquées, Succursale A, C.P. 6079, H3C 3A7, Montréal, Canada

    A. Fortin

  2. Département de Mathématiques et de Statistiques, Université Laval, G1K 7P4, Québec, Canada

    M. Fortin & J. J. Gervais

Authors
  1. A. Fortin
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  2. M. Fortin
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  3. J. J. Gervais
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Communicated by Roger Temam

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Fortin, A., Fortin, M. & Gervais, J.J. Complex transition to chaotic flow in a periodic array of cylinders. Theoret. Comput. Fluid Dynamics 3, 79–93 (1991). https://doi.org/10.1007/BF00271618

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  • DOI: https://doi.org/10.1007/BF00271618

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