Skip to main content
SpringerLink
Log in

Direct and repeated bifurcation into turbulence

  • Conference paper
  • First Online:
Approximation Methods for Navier-Stokes Problems

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 771))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ahlers, G. and Behringer, R. P. Evolution of turbulence from Rayleigh-Benard instability. Phys. Rev. Lett. 40, 712–716 (1978).

    Article  Google Scholar 

  2. Bowen, Rufus. A model for Couette flow data. Turbulence Seminar. Springer lecture notes in mathematics 615, 117–134, 1977.

    Article  MathSciNet  Google Scholar 

  3. Chenciner, A. and Iooss, G. Bifurcation de tores invariants. Arch. Rational Mech. Anal. 69, 109–198 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  4. Curry, J. H. A generalized Lorenz system. Commun. Math. Phys. 60, 193–204 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  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. 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, 1979

    Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  9. Iooss, G. and Joseph, D. D. Elementary stability and bifurcation theory (to appear).

    Google Scholar 

  10. Ito, A. Perturbation theory of self-oscillating system with a periodic perturbation. Prog. Theor. Phys. 61, 45 (1979)

    Article  Google Scholar 

  11. Successive subharmonic bifurcations and chaos in a nonlinear Mathieu equation. Prog. Theor. Phys. 61, 815 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  12. 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. Joseph, D. D. Stability of fluid motions Vols. I and II. Springer tracts in Nat. Phil. Vols. 27 and 28, 1976.

    Google Scholar 

  14. Libchaber, A. and Maurer, J. An experiment of Rayleigh-Benard in small domains; multiplation, locking and division of frequencies (to appear).

    Google Scholar 

  15. Lorenz, E. N. Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130 (1963).

    Article  Google Scholar 

  16. 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. 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. Ruelle D. and Takens, F. On the nature of turbulence. Comm. Math. Phys. 20, 167–192 (1971).

    Article  MathSciNet  MATH  Google Scholar 

  19. Sell, G. R. Bifurcation of higher dimensional tori. Arch. Rational Mech. Anal. 69, 199–230 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  20. Tomita K. and Kai, T. Phys. Letters 66A, 91 (1978).

    Article  MathSciNet  Google Scholar 

  21. Yavorskaya, I. M., Beleyayev, J. N., Monakov, A. A., Scherbakov, N. M. Generation of turbulence in a rotating visious fluid. JETP, 29, 329–334

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace Engineering and Mechanics, University of Minnesota, 55455, Minneapolis, MN

    Daniel D. Joseph

Authors
  1. Daniel D. Joseph
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Reimund Rautmann

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Joseph, D.D. (1980). Direct and repeated bifurcation into turbulence. In: Rautmann, R. (eds) Approximation Methods for Navier-Stokes Problems. Lecture Notes in Mathematics, vol 771. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086911

Download citation

  • DOI: https://doi.org/10.1007/BFb0086911

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09734-1

  • Online ISBN: 978-3-540-38550-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation