Abstract
In the framework of linear theory of instability the pattern instability is studied for a layer of a viscous fluid in a large aspect ratio container subject to vertically arbitrarily periodic excitation. As some applications, first the instabilities for Faraday water-wave system under excitations of the triangle and square waves are analyzed. Then, the relations between relative amplitudes and phase of the excitation, and the response modes of the patterns are investigated in the double-frequency Faraday experiment. The results are satisfactory.
Similar content being viewed by others
References
Miles, J., On Faraday waves,J. Fluid Mech., 1993, 248: 671.
Wu Junru,Observation of a non-propagating hydrodynamic soliton,Phys. Rev. Lett., 1984, 52: 1421.
Chen Weizhong, Wei Rongjue, Wang Benren, Parametrically excited internal wave breathers and kinds in liquids,Science in China, Ser. A, 1996, 39: 309.
Chen Weizhong, Wei Rongjue, Wang Benren, Chaos in nonpropagating hydrodynamical breathers,Phys. Rev., Ser. E, 1996, 53: 6016.
Christiansen, B., Alstrom, P., Levinsen, M.T., Ordered capillary-wave states: quasicrystals, hexagons, and radial waves,Phys. Rev. Lett., 1992, 68: 2157.
Edwards, W. S., Fauve, S., Patterns and quasi-patterns in the Faraday experiment,J. Fluid Mech., 1994, 278: 123.
ZhangWenbin, Vinals, J., Second instabilities and spatiotemporal chaos in parametric surface waves,Phys. Rev. Lett., 1995, 74: 690.
Kudrolli, A., Gollub, J.P., Localized spatiotemporal chaos in surface waves,Phys. Rev., Ser. E, 1996, 54: R1052.
Kumar, K., Linear theory of Faraday instability in viscous liquids,Proc. R. Soc. Lond., Ser. A, 1996, 452: 1113.
Müller, H. W., Analytic stability theory for Faraday waves and the observation of the harmonic surface response,Phys. Rev. Lett., 1997, 78: 2357.
Müller, H.W., Periodic triangular patterns in Faraday experiment,Phys. Rev. Lett., 1993, 71: 3287.
Cerda, E., Tirapegui, E., Faraday’s instability for viscous fluids,Phys. Rev. Lett., 1997, 78: 859.
Author information
Authors and Affiliations
Additional information
Project supported by the National Basic Research Project of Nonlinear Science and the Natural Science Foundation of Zhejiang Province.
Rights and permissions
About this article
Cite this article
Chen, W., Wei, R. Instability analysis for Faraday waves under arbitrarily periodic vibration. Sci. China Ser. A-Math. 41, 1302–1308 (1998). https://doi.org/10.1007/BF02882271
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02882271