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Sequences of infinite bifurcations and turbulence in a five-mode truncation of the Navier-Stokes equations

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Abstract

Two infinite sequences of orbits leading to turbulence in a five-mode truncation of the Navier-Stokes equations for a 2-dimensional incompressible fluid on a torus are studied in detail. Their compatibility with Feigenbaum's theory of universality in certain infinite sequences of bifurcations is verified and some considerations on their asymptotic behavior are inferred. An analysis of the Poincaré map is performed, showing how the turbulent behavior is approached gradually when, with increasing Reynolds number, no stable fixed point or periodic orbit is present and all the unstable ones become more and more unstable, in close analogy with the Lorenz model.

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Authors and Affiliations

  1. Istituto Matematico, Università di Modena, Modena, Italy

    Valter Franceschini

  2. Dipartimento di Matematica, Università di Ancona, Ancona, Italy

    Claudio Tebaldi

  3. Istituto di Fisica, Università di Bologna, Bologna, Italy

    Claudio Tebaldi

Authors
  1. Valter Franceschini
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  2. Claudio Tebaldi
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Franceschini, V., Tebaldi, C. Sequences of infinite bifurcations and turbulence in a five-mode truncation of the Navier-Stokes equations. J Stat Phys 21, 707–726 (1979). https://doi.org/10.1007/BF01107910

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  • DOI: https://doi.org/10.1007/BF01107910

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