Skip to main content
Log in

Chaos of liquid surface waves in a vessel under vertical excitation with slowly modulated amplitude

  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

Free surface waves in a cylinder of liquid under vertical excitation with slowly modulated amplitude are investigated in the current paper. It is shown by both theoretical analysis and numerical simulation that chaos may occur even for a single mode with modulation which can be used to explain Gollub and Meyer's experiment. The implied resonant mechanism accounting for this phenomenon is further elucidated.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Faraday M. On a peculiar class of acoustical figures and on certain forms assumed by groups of particles upon vibrating elastic surfaces.Phil Trans R Soc Lond, 1831, 121: 299–340

    Google Scholar 

  2. Miles J, Henderson D. Parametrically forced surface waves.Ann Rev Fluid Mech, 1990, 22: 143–165

    Article  MATH  MathSciNet  Google Scholar 

  3. Ciliberto S, Gollub JP. Chaotic mode competition in parametrically forced surface wave.J Fluid Mech, 1985, 158: 381–398

    Article  MathSciNet  Google Scholar 

  4. Kambe T, Umeki M. Nonlinear dynamics of two-mode interactions in parametric excitation of surface waves.J Fluid Mech, 1990, 212: 373–393

    Article  MATH  MathSciNet  Google Scholar 

  5. Gollub JP, Meyer CW. Symmetry-breaking instabilities on a fluid surface.Physica D, 1983,(6): 373–346

    Article  Google Scholar 

  6. Gollub JP, Ramshankar R. Spatiotemporal chaos in interfacial waves. in: Sirovich L. ed. New Perspective in Turbulence. New York: Springer-Verlag, 1993, 165–194

    Google Scholar 

  7. Miles JW. Nonlinear Faraday resonance.J Fluid Mech, 1984, 146: 285–302

    Article  MATH  MathSciNet  Google Scholar 

  8. Perko L. Differential Equation and Dynamical System. New York: Springer-Verlag, 1992

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guowei, H., Jiachun, L. Chaos of liquid surface waves in a vessel under vertical excitation with slowly modulated amplitude. Acta Mech Sinica 13, 106–112 (1997). https://doi.org/10.1007/BF02487916

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02487916

Key Words

Navigation