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Experimental study of the Faraday instability

  • S. Douady (a1)

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.

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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, 241267.
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, 505515.
Bogoliubov, N. N. & Mitropolsky, Y. A., 1961 Asymptotic Methods in the Theory of Non-Linear Oscillations, p. 267284. Gordon & Breach.
Ciliberto, S. & Gollub, J. P., 1984 Pattern competition leads to chaos. Phys. Rev. Lett. 52, 922925.
Ciliberto, S. & Gollub, J. P., 1985 Chaotic mode competition in parametrically forced surface waves. J. Fluid Mech. 158, 381398.
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.
Douady, S. & Fauve, S., 1988 Pattern selection in Faraday instability. Europhys. Lett. 6, 221226.
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, 129131 (transl. Sov. Phys. JETP 41, 157–160 (1986)).
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, 20702083 (transl. Sov. Phys. JETP 64, 1228–1236 (1986)).
Faraday, M.: 1831 On the forms and states of fluids on vibrating elastic surfaces. Phil. Trans. R. Soc. Lond. 52, 319340.
Gollub, J. P. & Meyer, C. W., 1983 Symmetry-breaking instabilities on a fluid surface. Physica D 6, 337346.
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, 553564.
Gu, X. M. & Sethna, P. R., 1987 Resonant surface waves and chaotic phenomena. J. Fluid Mech. 183, 543565.
Hsu, C. S.: 1977 On nonlinear parametric excitation problems. Adv. Appl. Mech. 17, 245302.
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, 11331136.
Leray, J. & Schauder, J., 1934 Topologie et equations fonctionnelles. Ann. Sci. Ecole Norm. Sup. (3) 51, 4578.
Meron, E.: 1987 Parametric excitation of multimode dissipative systems. Phys. Rev. A 35, 48924895.
Meron, E. & Procaccia, I., 1986a Theory of chaos in surface waves: the reduction from hydrodynamics to few-dimensional dynamics. Phys. Rev. Lett. 56, 13231326.
Meron, E. & Procaccia, I., 1986b Low-dimensional chaos in surface waves: theoretical analysis of an experiment. Phys. Rev. A 34, 32213237.
Miles, J. W.: 1984 Nonlinear Faraday resonance. J. Fluid Mech. 146, 285302.
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), 5058.
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, 14211424.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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