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Phase Locking in the Oscillations Leading to Turbulence

  • J. P. Gollub
  • S. V. Benson
Part of the Springer Series in Synergetics book series (SSSYN, volume 5)

Abstract

The transition to turbulence often occurs through one or more hydrodynamic instabilities, each characterized by the onset of a qualitatively distinct type of time dependence as a dimensionless parameter is varied. These phenomena have been studied in several different hydrodynamic systems, including circular Couette flow [1,2] and Rayleigh-Bénard convection[3–6]. The first appearance of time dependence often is a well-defined periodic oscillation. The mathematical techniques of nonlinear stability analysis have been used to predict the onset of oscillations, with some success [7]. However, these methods do not appear to be useful for predicting the onset or nature of more complex time-dependent phenomena, including nonperiodic motion.

Keywords

Prandtl Number Rayleigh Number Broadband Noise Hydrodynamic System Steady State Amplitude 
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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References

  1. 1.
    J.P. Gollub and H.L. Swinney, Phys. Rev. Lett. 35, 927 (1975)ADSCrossRefGoogle Scholar
  2. 1a.
    H.L. Swinney, P.R. Fenstermacher, and J.P. Gollub, in Synergetics, a Workshop, edited by H. Haken (Springer, Berlin, 1977); P.R. Fenstermacher, H.L. Swinney, and J. P. Gollub, J. Fluid Mech., to appear.Google Scholar
  3. 2.
    R.W. Waiden and R.J. Donnelly, Phys. Rev. Lett. 42, 301 (1979).ADSCrossRefGoogle Scholar
  4. 3.
    J.P. Gollub and S.V. Benson, Phys. Rev. Lett. 41, 948 (1978).ADSCrossRefGoogle Scholar
  5. 4.
    G. Ahlers and R.P. Behringer, Phys. Rev. Lett. 40, 712 (1978) and Progr. Theoret. Phys., in print.ADSCrossRefGoogle Scholar
  6. 5.
    P. Berge and M. Dubois, Optics Communications 21, 129 (1976).ADSCrossRefGoogle Scholar
  7. 6.
    A. Libchaber and J. Maurer, J. Physique Lett. 39, L-369 (1978).CrossRefGoogle Scholar
  8. 7.
    R.M. Clever and F.H. Busse, J. Fluid. Mech. 65, 625 (1974).ADSMATHCrossRefGoogle Scholar
  9. 8.
    D. Coles, J. Fluid Mech. 21, 385 (1965).ADSMATHCrossRefGoogle Scholar
  10. 9.
    B. van der Pol, Philos. Mag. 3, 65 (1927).Google Scholar
  11. 10.
    J.E. Flaherty and F.C. Hoppensteadt, Stud. Appl. Math. 55, 5 (1978).MathSciNetGoogle Scholar
  12. 11.
    J.P. Gollub, T.O. Brunner, and B.G. Danly, Science 200, 48 (1978).ADSCrossRefGoogle Scholar
  13. 12.
    A. Libchaber, private communication.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • J. P. Gollub
    • 1
  • S. V. Benson
    • 1
  1. 1.Physics DepartmentHaverford CollegeHaverfordUSA

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