Direct and repeated bifurcation into turbulence

  • Daniel D. Joseph
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 771)


Periodic Solution Rayleigh Number Couette Flow Steady Solution Taylor Vortex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Ahlers, G. and Behringer, R. P. Evolution of turbulence from Rayleigh-Benard instability. Phys. Rev. Lett. 40, 712–716 (1978).CrossRefGoogle Scholar
  2. [2]
    Bowen, Rufus. A model for Couette flow data. Turbulence Seminar. Springer lecture notes in mathematics 615, 117–134, 1977.MathSciNetCrossRefGoogle Scholar
  3. [3]
    Chenciner, A. and Iooss, G. Bifurcation de tores invariants. Arch. Rational Mech. Anal. 69, 109–198 (1979).MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Curry, J. H. A generalized Lorenz system. Commun. Math. Phys. 60, 193–204 (1978).MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Fenstermacher, P. R., Swinney, H. L. and Gollub, J. P. Dynamical instabilities and transition to chaotic Taylor vortex flow. J. Fluid Mech. (to appear).Google Scholar
  6. [6]
    Gollub, J. P. and Benson, S. V. Phase locking in the oscillations leading to turbulence. To appear in Pattern formation (approximate title), edited by H. Haken, Springer-Verlag, Berlin, 1979Google Scholar
  7. [7]
    Gollub, J. P. and Benson, S. V. Chaotic response to a periodic perturbation of a convecting fluid. Phys. Rev. Letters, 41, 948–950 (1978).CrossRefGoogle Scholar
  8. [8]
    Haken, H. Nonequilibrium phase transitons of limit cycles and multiperiodic flows. Z. Physik. B. 29, 61–66 (1978) and Nonequilibrium phase transitions of limit cycles and multiperiodic flow in continuous media. Z. Physik. B. 30, 423–428 (1978).CrossRefGoogle Scholar
  9. [9]
    Iooss, G. and Joseph, D. D. Elementary stability and bifurcation theory (to appear).Google Scholar
  10. [10]
    Ito, A. Perturbation theory of self-oscillating system with a periodic perturbation. Prog. Theor. Phys. 61, 45 (1979)CrossRefGoogle Scholar
  11. [10]a
    Successive subharmonic bifurcations and chaos in a nonlinear Mathieu equation. Prog. Theor. Phys. 61, 815 (1979).MathSciNetCrossRefzbMATHGoogle Scholar
  12. [11]
    Joseph, D. D. Hydrodynamic stability and bifurcation. In hydrodynamic instabilities and the transition to turbulence. Springer Topics in Current Physics. Eds. Swinney H. L. and Gollub, J. P.Google Scholar
  13. [12]
    Joseph, D. D. Stability of fluid motions Vols. I and II. Springer tracts in Nat. Phil. Vols. 27 and 28, 1976.Google Scholar
  14. [13]
    Libchaber, A. and Maurer, J. An experiment of Rayleigh-Benard in small domains; multiplation, locking and division of frequencies (to appear).Google Scholar
  15. [14]
    Lorenz, E. N. Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130 (1963).CrossRefGoogle Scholar
  16. [15]
    Maurer, J. and Libchaber, A. Rayleigh-Benard experiment in liquid helium; frequency locking and the onset of turbulence. J. Phys. Letters (to appear in July 1979).Google Scholar
  17. [16]
    Orszag, S. A. and Kelms, L. C. Transition to turbulence in Plane Poiseuille and Plane Couette Flow. J. Fluid Mech. (to appear).Google Scholar
  18. [17]
    Ruelle D. and Takens, F. On the nature of turbulence. Comm. Math. Phys. 20, 167–192 (1971).MathSciNetCrossRefzbMATHGoogle Scholar
  19. [18]
    Sell, G. R. Bifurcation of higher dimensional tori. Arch. Rational Mech. Anal. 69, 199–230 (1979).MathSciNetCrossRefzbMATHGoogle Scholar
  20. [19]
    Tomita K. and Kai, T. Phys. Letters 66A, 91 (1978).MathSciNetCrossRefGoogle Scholar
  21. [20]
    Yavorskaya, I. M., Beleyayev, J. N., Monakov, A. A., Scherbakov, N. M. Generation of turbulence in a rotating visious fluid. JETP, 29, 329–334Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Daniel D. Joseph
    • 1
  1. 1.Department of Aerospace Engineering and MechanicsUniversity of MinnesotaMinneapolis

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