Incipient Turbulence and Chaos

  • Giovanni Gallavotti
Part of the Texts and Monographs in Physics book series (TMP)


Analysing the fundamental problems of the NS equation has, in particular, brought up clearly the lack of an adequate algorithm, i.e. convergent and constructive, for its solution. Furthermore even if we knew that the fluid equations had unique and regular solutions, for regular initial data (for the NS equation this is true if d = 2 and likely if d = 3, but false if d >4) this would not help much in the understanding of the physical properties of such solutions at large times.


Periodic Orbit Hopf Bifurcation Periodic Motion Rotation Number Period Doubling Bifurcation 
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  1. [FT79]
    Franceschini, V., Tebaldi, C Sequences of infinite bifurcations and tur-bulence in a five-mode truncation of the Navier Stokes equations,Journal of Statistical Physics, 21 707–726, 1979: reprinted inGoogle Scholar
  2. [FGN88]
    Franceschini, V., Giberti, C., Nicolini M.: Common periodic behavior in larger and larger truncations of the Navier Stokes equations, Journal of Statistical Physics, 50, 879–896, 1988.MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. [Fr80]
    Franceschini, V A Feigenbaum sequence of bifurcations in the Lorenz model,Journal of Statistical Physics, 22 397–406, 1980.Google Scholar
  4. [Ri82]
    Riela, G.: A new six mode truncation of the Navier Stokes equations on a two dimensional torus: a numerical study,Nuovo Cimento, 69B 245, 1982.Google Scholar
  5. [Ga83]
    Gallavotti, G.: The elements of mechanics,1983, Springer Verlag (Texts and monographs in Physics).Google Scholar
  6. [FSG79]
    Fenstermacher, F., Swinney, H., Gollub J.: Dynamical instabilities and the transition to chaotic Taylor vortex flow, Journal of Fluid Mechanics, 94, 103–128, 1979.ADSCrossRefGoogle Scholar
  7. [SG78]
    Swinney, H., Gollub, J., P.: The transition to turbulence, Physics Today, 31, 41–49, 1978.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Giovanni Gallavotti
    • 1
  1. 1.Dipartmento di Fisica, I.N.F.N.Università degli Studi di Roma “La Sapienza”RomaItaly

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