Skip to main content

Instability of Two-Dimensional Standing Faraday Waves

  • Conference paper
IUTAM Symposium on Free Surface Flows

Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 62))

Abstract

The nonlinear inst ability of Faraday waves may be examined either by decomposition into standing-wave modes, as in Craik (1994, 1998), Craik & Armitage (1995b) and Decent & Craik (1999); or by means of counter-propagating wave envelopes, as in recent work of Martel, Knoblo ch & Vega (2000). The differences and equivalences of these approaches are explored, and some results reinterpret ed.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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

  • Craik, A.D.D. 1994 The stability of some three-dimensional and time-dependent flows. In Nonlinear Instability of Nonparallel Flows (eds. S.P. Lin & W. Phillips) pp. 382–396. (Proc. IUTAM Symp., Potsdam, NY. July 1993) Springer.

    Google Scholar 

  • Craik, A.D.D. & Armitage, J. 1995a Faraday excitation, hysteresis and wave instability in a narrow rectangular wave tank. Fluid Dyn. Res., 15, pp. 129–143.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Craik, A.D.D. & Armitage, J. 1995b ‘Hysteresis and interaction of standing waves with Faraday excitation’. In Asymptotic Modelling in Fluid Mechanics (eds. P.-A. Bois, E. Derait, R. Gatignol, A. Rigolot) pp.117–128 (Proc. Colloque en l’honneur de J.P. Guiraud, Paris 1994) Springer.

    Google Scholar 

  • Craik, A.D.D. 1998 ‘Nonlinear interaction of standing waves with Faraday excitation’. In Nonlinear Instability, Chaos and Turbulence You, (eds. L. Debnath & D.N. Riahi) Ch. 4, 91–127. Computational Mechanics Publ. WIT Press, UK.

    Google Scholar 

  • Decent, S.P. & Craik, A.D.D. 1995 Hysteresis in Faraday resonance. J. Fluid Mech., 293, pp. 237–268.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Decent, S.P. & Craik, A.D.D. 1997 On limit cycles arising from the parametric excitation of standing waves. Wave Motion 25, 275–294.

    Article  MathSciNet  MATH  Google Scholar 

  • Decent, S.P. & Craik, A.D.D. 1999 Sideband instability and modulations of Faraday waves. Wave Motion 30, 43–55.

    Article  MathSciNet  MATH  Google Scholar 

  • Douady, S., Fauve, S. & Thual, O. 1989 Oscillatory phase modulation of parametrically forced surface waves. Europhys. Lett., 10(4), pp. 309–315.

    Article  ADS  Google Scholar 

  • Knobloch, E. & De Luca, J. 1990 Amplitude equations for travelling wave convection. Nonlinearity 3, 975–980.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Martel, C., Knobloch, E. & Vega, J.M. 2000 Dynamics of counterpropagating waves in parametrically forced systems. Physica D 137, 94–123.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Martel, C. & Vega, J.M. 1996 Finite size effects near the onset of the oscillatory instability. Nonlinearity 9, 1129–1171.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Martel, C. & Vega, J.M. 1998 Dynamics of a hyperbolic system that applies at the onset of the oscillatory instability. Nonlinearity 11, 105–142.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Miles, J.W. & Henderson, D. 1990 Parametrically forced surface waves. Ann. Rev. Fluid Mech., 22, pp. 143–165.

    Article  MathSciNet  ADS  Google Scholar 

  • Miles, J.W. 1993 On Faraday waves. J. Fluid Mech. 248, 671–683. [Corrigendum: J. Fluid Mech. 269, 372 (1994)].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Milner, S.T. 1991 Square patterns and secondary instabilities in driven capillary waves. J. Fluid Mech. 225, 81–100.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Pierce, R.D. & Knobloch, E. 1994 On the modulational stability of travelling and standing waves. Phys. Fluids 6, 1177–1190.

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media Dordrecht

About this paper

Cite this paper

Craik, A.D.D. (2001). Instability of Two-Dimensional Standing Faraday Waves. In: King, A.C., Shikhmurzaev, Y.D. (eds) IUTAM Symposium on Free Surface Flows. Fluid Mechanics and Its Applications, vol 62. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0796-2_9

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-0796-2_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-3854-6

  • Online ISBN: 978-94-010-0796-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics