A simple model for Faraday waves

American Journal of Physics

Volumn 64, Issue 12, 1996, Pages 1482-1487

  Bechhoefer, John ^a   Johnson, Brad ^b  

^a SIMON FRASER UNIVERSITY   (Canada)

^b WESTERN WASHINGTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030492698     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18412     Document Type: Article

References (23)

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3. A. B. Ezersky, M. I. Rabinovich, V. P. Reutov, and I. M. Starobinets, "Spatiotemporal chaos in the parametric excitation of a capillary ripple," Sov. Phys. JETP 64, 1228-1236 (1986).
4. B. Christiansen, P. Alstrøm, and M. T. Levinsen, "Ordered capillary-wave states: Quasicrystals, hexagons, and radial waves," Phys. Rev. Lett. 68, 2157-2160 (1992).
5. S. Fauve, K. Kumar, C. Laroche, D. Beysens, and Y. Garrabos, "Parametric instability of a liquid-vapor interface close to the critical point," Phys. Rev. Lett. 68, 3160-3163 (1992).
6. W. S. Edwards and S. Fauve, "Patterns and quasi-patterns in the Faraday experiment," J. Fluid Mech. 278, 123-148 (1994).
7. E. Bosch and W. van de Water, "Spatiotemporal intermittency in the Faraday experiment," Phys. Rev. Lett. 70, 3420-3423 (1993).
8. B. J. Gluckman, C. B. Arnold, and J. P. Gollub, "Statistical studies of chaotic wave patterns," Phys. Rev. E 51, 1128-1147 (1995).
9. L. Daudet, V. Ego, S. Manneville, and J. Bechhoefer, "Secondary instabilities of surface waves on viscous fluids in the Faraday instability," Europhys. Lett. 32, 313-318 (1995).
10. C. S. Hsu, "Impulsive parametric excitation: Theory," J. Appl. Mech. 39, 551-558 (1972).
11. E. D. Yorke, "Square-wave model for a pendulum with oscillating suspension," Am. J. Phys. 46, 285-288 (1978).
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13. K. Kumar and K. L. S. Tuckerman, "Parametric instability of the interface between two fluids," J. Fluid Mech. 279, 49-68 (1994); cf. J. Beyer and R. Friedrich, "Faraday instability: Linear analysis for viscous fluids," Phys. Rev. E 51, 1162-1168 (1995).
14. K. Kumar and K. L. S. Tuckerman, "Parametric instability of the interface between two fluids," J. Fluid Mech. 279, 49-68 (1994); cf. J. Beyer and R. Friedrich, "Faraday instability: Linear analysis for viscous fluids," Phys. Rev. E 51, 1162-1168 (1995).
15. Lord Rayleigh, "On maintained vibrations," Philos. Mag. 15, 229-235 (1883); "On the crispations of fluid resting upon a vibrating support," ibid. 16, 50-58 (1883). Reprinted in Scientific Papers by Lord Rayleigh (Dover, New York, 1964), Vol. II, pp. 188-193 and 212-219.
16. Lord Rayleigh, "On maintained vibrations," Philos. Mag. 15, 229-235 (1883); "On the crispations of fluid resting upon a vibrating support," ibid. 16, 50-58 (1883). Reprinted in Scientific Papers by Lord Rayleigh (Dover, New York, 1964), Vol. II, pp. 188-193 and 212-219.
17. Lord Rayleigh, "On maintained vibrations," Philos. Mag. 15, 229-235 (1883); "On the crispations of fluid resting upon a vibrating support," ibid. 16, 50-58 (1883). Reprinted in Scientific Papers by Lord Rayleigh (Dover, New York, 1964), Vol. II, pp. 188-193 and 212-219.
18. J. Bechhoefer, V. Ego, S. Manneville, and B. Johnson, "An experimental study of the onset of parametrically pumped surface waves in viscous fluids," J. Fluid Mech. 288, 325-350 (1995).
19. The electromagnetic shaker tables that are usually used to generate Faraday waves will not give an accurate output if a function generator is used to create the triangle wave. Because of the inductance of the vibration coils, the different frequency components of the input wave form will have different phase shifts and the result will be far from a triangle wave. A straightforward workaround is to use the feedback system of Ref. 6, which requires a modest amount of programing. Alternatively, one could design a vibrator specifically for triangle waveforms.
20. S. T. Milner, "Square patterns and secondary instabilities in driven capillary waves," J. Fluid Mech. 225, 81-100 (1991).
21. W. Zhang, "Pattern formation in weakly damped parametric surface waves," Ph.D. thesis, Florida State University, 1994; W. Zhang and J. Viñals, "Square patterns and quasipatterns in weakly damped Faraday waves," Phys. Rev. E 53, R4283 (1996).
22. W. Zhang, "Pattern formation in weakly damped parametric surface waves," Ph.D. thesis, Florida State University, 1994; W. Zhang and J. Viñals, "Square patterns and quasipatterns in weakly damped Faraday waves," Phys. Rev. E 53, R4283 (1996).
23. L. Debnath, Nonlinear Water Waves (Academic, San Diego, 1994), pp. 62-66.