The taylor-green vortex : Fully developed turbulence and transition to spatial chaos

  • Uriel Frisch
Seminars and Communications
Part of the Lecture Notes in Physics book series (LNP, volume 179)


A brief introduction to fully developed turbulence is given (cf. Refs. 1-2). We then report results obtained from numerical simulations of the Taylor-Green three dimensional vortex flow 3. This flow is perhaps the simplest system in which one can study the generation of small scales by three-dimensional vortex stretching and the resulting turbulence. The problem is studied by both direct spectral numerical solution of the Navier-Stokes equations (with up to 2563 modes) and by power series analysis in time.


High Reynolds Number Vortex Line Vortex Sheet Inertial Range Real Singularity 
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    U. Frisch, P.L. Sulem and M. Nelkin, J. Fluid Mech. 87, 719 (1978).Google Scholar
  2. 2.
    U. Frisch in Chaotic Behaviour in Deterministic Systems, Les Houches 1981, North Holland (in press).Google Scholar
  3. 3.
    M. Brachet, D. Meiron, S. Orszag, B. Nickel, R. Morf and U. Frisch, Small-scale structure of the Taylor-Green vortex, J. Fluid Mech. in Dress (1982 or 1983).Google Scholar
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    R. Morf, S. Orszag and U. Frisch, Phys. Rev. Lett. 44, 572 (1980).CrossRefGoogle Scholar
  5. 5.
    M. Henon, C. R. Acad. Sci. 262, 312 (1966).Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Uriel Frisch
    • 1
  1. 1.CNRS, Observatoire de NiceNice CedexFrance

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