Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 39
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Pototsky, Andrey and Bestehorn, Michael 2016. Faraday instability of a two-layer liquid film with a free upper surface. Physical Review Fluids, Vol. 1, Issue. 2,


    Noskov, Roman E. Smirnova, Daria A. and Kivshar, Yuri S. 2013. Subwavelength solitons and Faraday waves in two-dimensional lattices of metal nanoparticles. Optics Letters, Vol. 38, Issue. 14, p. 2554.


    Argentina, Médéric and Iooss, Gérard 2012. Quasipatterns in a parametrically forced horizontal fluid film. Physica D: Nonlinear Phenomena, Vol. 241, Issue. 16, p. 1306.


    Maksimov, A. O. and Leighton, T. G. 2012. Pattern formation on the surface of a bubble driven by an acoustic field. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 468, Issue. 2137, p. 57.


    Friend, James and Yeo, Leslie Y. 2011. Microscale acoustofluidics: Microfluidics driven via acoustics and ultrasonics. Reviews of Modern Physics, Vol. 83, Issue. 2, p. 647.


    Friend, James and Yeo, Leslie 2010. Using laser Doppler vibrometry to measure capillary surface waves on fluid-fluid interfaces. Biomicrofluidics, Vol. 4, Issue. 2, p. 026501.


    Zakaria, Kadry 2008. Standing waves between immiscible liquids inside an infinite boxed basin. Journal of Physics A: Mathematical and Theoretical, Vol. 41, Issue. 17, p. 175501.


    Ikeda, Takashi 2007. Autoparametric resonances in elastic structures carrying two rectangular tanks partially filled with liquid. Journal of Sound and Vibration, Vol. 302, Issue. 4-5, p. 657.


    Ben-David, Oded Assaf, Michael Fineberg, Jay and Meerson, Baruch 2006. Experimental Study of Parametric Autoresonance in Faraday Waves. Physical Review Letters, Vol. 96, Issue. 15,


    Assaf, Michael and Meerson, Baruch 2005. Parametric autoresonance in Faraday waves. Physical Review E, Vol. 72, Issue. 1,


    Jian, Yongjun and E, Xuequan 2005. Instability analysis of nonlinear surface waves in a circular cylindrical container subjected to a vertical excitation. European Journal of Mechanics - B/Fluids, Vol. 24, Issue. 6, p. 683.


    Kumar, K Bandyopadhyay, A and Mondal, G. C 2004. Parametric instability in a fluid with temperature-dependent surface tension. Europhysics Letters (EPL), Vol. 65, Issue. 3, p. 330.


    Ubal, S. Giavedoni, M. D. and Saita, F. A. 2003. A numerical analysis of the influence of the liquid depth on two-dimensional Faraday waves. Physics of Fluids, Vol. 15, Issue. 10, p. 3099.


    Wright, P. H. and Saylor, J. R. 2003. Patterning of particulate films using Faraday waves. Review of Scientific Instruments, Vol. 74, Issue. 9, p. 4063.


    KNOBLOCH, EDGAR MARTEL, CARLOS and VEGA, JOSE M. 2002. Coupled Mean Flow-Amplitude Equations for Nearly Inviscid Parametrically Driven Surface Waves. Annals of the New York Academy of Sciences, Vol. 974, Issue. 1, p. 201.


    Tyvand, P.A. 2002. Transport Phenomena in Porous Media II.


    Vega, José M. Knobloch, Edgar and Martel, Carlos 2001. Nearly inviscid Faraday waves in annular containers of moderately large aspect ratio. Physica D: Nonlinear Phenomena, Vol. 154, Issue. 3-4, p. 313.


    Chen, Peilong and Wu, Kuo-An 2000. Subcritical Bifurcations and Nonlinear Balloons in Faraday Waves. Physical Review Letters, Vol. 85, Issue. 18, p. 3813.


    Perlin, Marc and Schultz, William W. 2000. Capillary Effects on Surface Waves. Annual Review of Fluid Mechanics, Vol. 32, Issue. 1, p. 241.


    Chen, Peilong and Viñals, Jorge 1999. Amplitude equation and pattern selection in Faraday waves. Physical Review E, Vol. 60, Issue. 1, p. 559.


    ×
  • Journal of Fluid Mechanics, Volume 248
  • March 1993, pp. 671-683

On Faraday waves

  • John Miles (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112093000965
  • Published online: 01 April 2006
Abstract

The standing waves of frequency ω and wavenumber κ that are induced on the surface of a liquid of depth d that is subjected to the vertical displacement ao cos 2wt are determined on the assumptions that: the effects of lateral boundaries are negligible; ε = ka0 tanh kd [Lt ] 1 and 0 < ε−δ = O(δ3), where δ is the linear damping ratio of a free wave of frequency ω; the waves form a square pattern (which follows from observation). This problem, which goes back to Faraday (1831), has recently been treated by Ezerskii et al. (1986) and Milner (1991) in the limit of deep-water capillary waves (kd, kl* [Gt ] 1, where l* is the capillary length). Ezerskii et al. show that the square pattern is unstable for sufficiently large ε—δ, and Milner shows that nonlinear damping is necessary for equilibration of the square pattern. The present formulation extends those of Ezerskii et al. and Milner to capillary–gravity waves and finite depth and incorporates third-order parametric forcing, which is neglected in these earlier formulations but is comparable with third-order damping. There are quantitative differences in the resulting evolution equations (for kd, kl* [Gt ] 1), which appear to reflect errors in the earlier work.

These formulations determine a locus of admissible waves, but they do not select a particular wave. The hypothesis that the selection process maximizes the energy-transfer rate to the Faraday wave selects the maximum of the resonance curve in a frequency-amplitude plane.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax