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Experimental study of the Faraday instability

Published online by Cambridge University Press:  26 April 2006

S. Douady
S. Douady
Affiliation:
Laboratoire de Physique de l'Ecole Normale Supérieure de Lyon, 46 Allée d'Italie, 69364 Lyon Cedex 07, France
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Abstract

An experimental study of surface waves parametrically excited by vertical vibrations is presented. The shape of the eigenmodes in a closed vessel, and the importance of the free-surface boundary conditions, are discussed. Stability boundaries, wave amplitude, and perturbation characteristic time of decay are measured and found to be in agreement with an amplitude equation derived by symmetry. The measurement of the amplitude equation coefficients explains why the observed transition is always supercritical, and shows the effect of the edge constraint on the dissipation and eigen frequency of the various modes. The fluid surface tension is obtained from the dispersion relation measurement. Several visualization methods in large-aspect-ratio cells are presented.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 221 , December 1990 , pp. 383 - 409
Copyright
© 1990 Cambridge University Press

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References

Batchelor, G. K.: 1967 An introduction to Fluid Dynamics. §5.13. Cambridge University Press.
Benjamin, T. B. & Scott, J. C., 1979 Gravity-capillary waves with edge constraints. J. Fluid Mech. 92, 241–267.Google Scholar
Benjamin, T. B. & Ursell, F., 1954 The stability of the plane free surface of a liquid in vertical periodic motion. Proc. R. Soc. Lond. A 225, 505–515.Google Scholar
Bogoliubov, N. N. & Mitropolsky, Y. A., 1961 Asymptotic Methods in the Theory of Non-Linear Oscillations, p. 267–284. Gordon & Breach.
Ciliberto, S. & Gollub, J. P., 1984 Pattern competition leads to chaos. Phys. Rev. Lett. 52, 922–925.Google Scholar
Ciliberto, S. & Gollub, J. P., 1985 Chaotic mode competition in parametrically forced surface waves. J. Fluid Mech. 158, 381–398.Google Scholar
Douady, S.: 1988 Capillary-gravity surface wave modes in a closed vessel with edge constraint: eigen-frequency and dissipation. Woods Hole Ocean. Inst. Tech. Rep. WHOI-88–26.Google Scholar
Douady, S. & Fauve, S., 1988 Pattern selection in Faraday instability. Europhys. Lett. 6, 221–226.Google Scholar
Ezerskii, A. B., Korotin, P. I. & Rabinovitch, M. I., 1985 Random self-modulation of two-dimensional structures on a liquid surface during parametric excitation. Zh. Eksp. Teor. Fiz. 41, 129–131 (transl. Sov. Phys. JETP 41, 157–160 (1986)).Google Scholar
Ezerskii, A. B., Rabinovich, M. I., Reutov, V. P. & Starobinets, I. M., 1986 Spatiotemporal chaos in the parametric excitation of a capillary ripple. Zh. Eksp. Teor. Fiz. 91, 2070–2083 (transl. Sov. Phys. JETP 64, 1228–1236 (1986)).Google Scholar
Faraday, M.: 1831 On the forms and states of fluids on vibrating elastic surfaces. Phil. Trans. R. Soc. Lond. 52, 319–340.Google Scholar
Gollub, J. P. & Meyer, C. W., 1983 Symmetry-breaking instabilities on a fluid surface. Physica D 6, 337–346.Google Scholar
Graham-Eagle, J. G.: 1983 A new method for calculating eigenvalues with application to gravity-capillary waves with edge constraints. Math. Proc. Camb. Phil. Soc. 94, 553–564.Google Scholar
Gu, X. M. & Sethna, P. R., 1987 Resonant surface waves and chaotic phenomena. J. Fluid Mech. 183, 543–565.Google Scholar
Hsu, C. S.: 1977 On nonlinear parametric excitation problems. Adv. Appl. Mech. 17, 245–302.Google Scholar
Keolian, R., Turkevich, L. A., Putterman, S. J., Rudnick, I. & Rudnick, J. A., 1984 Subharmonic sequences in the Faraday experiment: departure from period doubling. Phys. Rev. Lett. 47, 1133–1136.Google Scholar
Leray, J. & Schauder, J., 1934 Topologie et equations fonctionnelles. Ann. Sci. Ecole Norm. Sup. (3) 51, 45–78.Google Scholar
Meron, E.: 1987 Parametric excitation of multimode dissipative systems. Phys. Rev. A 35, 4892–4895.Google Scholar
Meron, E. & Procaccia, I., 1986a Theory of chaos in surface waves: the reduction from hydrodynamics to few-dimensional dynamics. Phys. Rev. Lett. 56, 1323–1326.Google Scholar
Meron, E. & Procaccia, I., 1986b Low-dimensional chaos in surface waves: theoretical analysis of an experiment. Phys. Rev. A 34, 3221–3237.Google Scholar
Miles, J. W.: 1984 Nonlinear Faraday resonance. J. Fluid Mech. 146, 285–302.Google Scholar
Nayfeh, A. H. & Mook, D. T., 1979 Nonlinear Oscillations, §1.5 and 5.7.3. Wiley.
Rayleigh, Lord: 1883 On the crispation of fluid resting upon a vibrating support. Phil. Mag. 15, (5), 50–58.Google Scholar
Whitham, G. B.: 1974 Linear and Nonlinear Waves. Wiley-Interscience.
Wu, J., Keolian, R. & Rudnick, I., 1984 Observation of a nonpropagating hydrodynamic soliton. Phys. Rev. Lett. 52, 1421–1424.Google Scholar