Characterizing Dynamical Complexity in Interfacial Waves

  • J. P. Gollub
Part of the NATO ASI Series book series (NSSB, volume 208)


Waves on a fluid interface may be excited parametrically by vertical excitation of the container (Faraday, 1831). These waves illustrate the full spectrum of dynamical complexity, including stationary patterns, periodically or chaotically oscillating patterns, and spatiotemporal chaos. A variety of experiments performed at Haverford and illustrating these phenomena are reviewed, with emphasis on the development of methods for studying complex dynamics. A general review of this problem has been given by Miles & Henderson (1990).


Orientational Order Vertical Excitation Interfacial Wave Spatiotemporal Chaos Rectangular Container 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Benjamin, T.B. Ursell, F., 1954, The stability of the plane free surface of a liquid in vertical periodic motion, Proc. R Soc. Lond A225: 505.MathSciNetzbMATHGoogle Scholar
  2. Ciliberto, S. & Gollub, J.P., 1984, Pattern competition leads to chaos, Phys. Rev. Lett. 52: 922.CrossRefGoogle Scholar
  3. Ciliberto, S. Gollub, J.P., 1985, Chaotic mode competition in parametrically forced surface waves, J. Fluid Mech., 158: 381.MathSciNetCrossRefGoogle Scholar
  4. Faraday, M., 1831, On the forms and states assumed by fluids in contact with vibrating elastic surfaces, Phil. Trans. R Soc. Lond., 121: 319.Google Scholar
  5. Funakoshi, M. Inoue, S., 1988, Surface waves due to resonant horizontal oscillation, J. Fluid Mech., 192: 219.MathSciNetGoogle Scholar
  6. Gollub, J.P. Meyer, C.W., 1983, Symmetry-breaking instabilities on a fluid surface, Physica D, 6: 337.Google Scholar
  7. Gollub, J.P. Ramshankar, R., 1990, Spatiotemporal chaos in interfacial waves, in: “New Perspectives in Turbulence,” S. Orszag and L Sirovich, ed., Springer-Verlag, Berlin.Google Scholar
  8. Miles, J. Henderson, 1990, Parametrically forced surface waves, Ann. Rev. Fluid Mech., to appear.Google Scholar
  9. Silber, M. Knobloch, E., 1989, Parametrically excited surface waves in square geometry, to appear.Google Scholar
  10. Simonelli, F. Gollub, J.P., 1989, Surface wave mode interactions: effects of symmetry and degeneracy, J. Fluid Mech. 199: 471.MathSciNetCrossRefGoogle Scholar
  11. Tufillaro, N.B., Ramshankar, R., Gollub, J.P., 1989, Order-Disorder Transition in Capillary Ripples, Phys. Rev. Lett. 62: 422.CrossRefGoogle Scholar
  12. Umeki, M., 1990, Faraday resonance in rectangular geometry, J. Fluid Mech., to appear.Google Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • J. P. Gollub
    • 1
    • 2
  1. 1.Physics DepartmentHaverford CollegeHaverfordUSA
  2. 2.David Rittenhouse LaboratoryThe University of PennsylvaniaPhiladelphiaUSA

Personalised recommendations