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)


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.


Prandtl Number Rayleigh Number Broadband Noise Hydrodynamic System Steady State Amplitude 
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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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