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Journal of Statistical Physics

, Volume 21, Issue 6, pp 707–726 | Cite as

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

  • Valter Franceschini
  • Claudio Tebaldi
Articles

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.

Key words

Navier-Stokes equations turbulence strange attractors Poincarè map infinite sequences of periodic orbits stable and hyperbolic orbits collapse universal properties in infinite sequences of bifurcations 

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Copyright information

© Plenum Publishing Corporation 1979

Authors and Affiliations

  • Valter Franceschini
    • 1
  • Claudio Tebaldi
    • 2
    • 3
  1. 1.Istituto MatematicoUniversità di ModenaModenaItaly
  2. 2.Dipartimento di MatematicaUniversità di AnconaAnconaItaly
  3. 3.Istituto di FisicaUniversità di BolognaBolognaItaly

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