Faraday's instability in viscous fluid

Journal of Fluid Mechanics

Volumn 368, Issue , 1998, Pages 195-228

  Cerda, E A ^a,b,d   Tirapegui, E L ^b,c  

^a UNIVERSIDAD DE SANTIAGO DE CHILE   (Chile)

^b Ctro Fis No Lineal y Sist C   (Chile)

^c DEPARTAMENTO DE FÍSICA   (Chile)

^d MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AMPLIFICATION; APPROXIMATION THEORY; COMPUTATIONAL FLUID DYNAMICS; SURFACE WAVES;

DIFFERENTIAL KINEMATICAL VISCOSITY; FARADAY'S INSTABILITY; MATHIEU EQUATION; RAYLEIGH-TAYLOR INSTABILITY;

VISCOSITY OF LIQUIDS;

EID: 0032137989     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112098001578     Document Type: Article

References (40)

1. BECHHOEFER, J., EGO, V., MANNEVILLE, S. & JOHNSON, B. 1995 An experimental study of the onset of parametrically pumped surface waves in viscous fluids. J. Fluid Mech. 288, 325-350.
2. 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.
3. BERGÉ, P., POMEAU, Y. & VIDAL, C. 1984 Oscillateur libre-oscillateur amorti. In L'ordre dans le Chaos. Hermman.
4. BESSON, T., EDWARDS, W. S. & TUCKERMAN, L. S. 1996 Two-frequency parametric excitation of surface waves. Phys. Rev. E 54, 507-513.
5. BEYER, J. & FRIEDRICH, R. 1995 Faraday instability: Linear analysis for viscous fluids. Phys. Rev. E 51, 1162-1168.
6. CERDA, E. & TIRAPEGUI, E. 1997a Faraday's instability for viscous fluids. Phys. Rev. Lett. 78, 859-863.
7. CERDA, E. & TIRAPEGUI, E. 1997b On the linear evolution of the surface of a viscous incompressible fluid. Bull. l'Acad. R. Sci. de Belgique (Classe des Sciences 7/12/1996).
8. CHANDRASEKAR, H. 1981 Hydrodynamic and Hydromagnetic Stability, chap. 10. Dover.
9. CHEN, P. & VIÑALS, J. 1997 Pattern selection in Faraday waves. Phys. Rev. Lett. 14, 2670-2673.
10. CILIBERTO, S. & GOLLUB, J. P. 1985 Phenomenological model of chaotic mode competition in surface waves. Nuovo Cimento 6D, 309-316.
11. DOUADY, S. 1989 Instabilite parametrique d'ondes de surface. PhD thesis, Paris VI, Paris.
12. DOUADY, S. & FAUVE, S. 1988 Pattern selection in Faraday instability. Europhys. Lett. 6, 221-226.
13. EDWARDS, W. S. & FAUVE, S. 1992 Parametric instability of a liquid-vapor interface close to the critical point. Phys. Rev. Lett. 68, 3160-3164.
14. EDWARDS, W. S. & FAUVE, S. 1993 Parametrically excited quasicrystalline surface waves. Phys. Rev. E 47, 788-791.
15. EDWARDS, W. S. & FAUVE, S. 1994 Patterns and quasi-patterns in the Faraday experiment. J. Fluid Mech. 278, 123-148.
16. EISENMENGER, W. 1959 Dynamics properties of the surface tension of water and aqueous solutions of surface active agents with standing capillary waves in the frequency range 10 kc/s to 1.5 Mc/s. Acustica 9, 328-340.
17. ELPHICK, C. & MERON, E. 1989 Localized structures in surface waves. Phys. Rev. A 40, 3226-3229.
18. GENNES, P. G. DE 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827-863.
19. GOLDMAN, I. I. & KRIVCHENKOV, V. D. 1961 Problems in Quantum Mechanics. Adison Wesley.
20. KUDROLLI, A. & GOLLUB, J. P. 1996 Pattern and spatiotemporal chaos in parametrically forced surface waves: a systematic survey at large aspect ratio. Physica D 97, 133-154.
21. KUMAR, K. 1996 Linear theory of Faraday instability in viscous liquids. Proc. R. Soc. Lond. A 452. 1113-1126.
22. KUMAR, K. & TUCKERMAN, L. S. 1994 Parametric instability of the interface between two fluids. J. Fluid Mech. 279, 49-68.
23. LANDAU, L. D. & LIFSHITZ, E. M. 1970 Parametric resonance. In Mechanica. Reverté.
24. LANDAU, L. D. & LIFSHITZ, E. M. 1987 Fluid Mechanics. Pergamon.
25. LIOUBASHEVSKY, O., ARBELL, H. & FINEBERG, J. 1996 Dissipative solitary states in driven surface waves. Phys. Rev. Lett. 76, 3959-3963.
26. LIOUBASHEVSKY, O., FINEBERG, J. & TUCKERMAN, L. S. 1997 Scaling of the transition to parametrically driven surface waves in highly dissipative systems. Phys. Rev. E 55, 3832-3835.
27. MARKUSHEVICH, A. I. 1970 Continuación Analítica en una Estrella. In Teoría de las Funciones Analíticas. Vol. 2. Mir.
28. MELO, F., UMBANHOWAR, P. & SWINNEY, H. L. 1994 Transition to parametric wave patterns in a vertically oscillated granular layer. Phys. Rev. Lett. 72, 172-176.
29. MELO, F., UMBANHOWAR, P. & SWINNEY, H. L. 1995 Hexagons, kinks, and disorder in oscillated granular layers. Phys. Rev. Lett. 75, 3838.
30. MESSIAH, A. 1961 Quantum Mechanics, Vol. 1. North Holland.
31. MORSE, P. M. & FESHBACH, H. 1953 Methods of Theoretical Physics. Vol. 1, Chap. 5. McGraw Hill.
32. MüLLER, H. W. 1993 Periodic triangular patterns in the Faraday experiment. Phys. Rev. Lett. 71, 3287-3291.
33. MüLLER, H. W., WITTMER, H., WAGNER, C., ALBERS, J. & KNORR, K. 1997 Analytic stability theory for Faraday waves and the observation of the harmonic surface response. Phys. Rev. Lett. 78, 2357-2360.
34. PUSHKAREV, A. N. & ZAKHAROV V. E. 1996 Turbulence of capillary waves. Phys. Rev. Lett. 76, 3320-3324.
35. SCHRÖDER, E., ANDERSEN, J. S., LEVINSEN, M. T., ALSTROM, P. & GOLDBURG, W. I. 1996 Relative particle motion in capillary waves. Phys. Rev. Lett. 76, 4717-4721.
36. SOROKIN, V. I. 1957 The effects of fountain formation at the surface of a vertically oscillating liquid. Sov. Phys. Acoust. 3, 281-295.
37. UMBANHOWAR, P., MELO, F. & SWINNEY, H. L. 1996 Localized excitations in a vertically vibrated granular layer. Nature 382, 793.
38. WU, J., KEOLIAN, R. & RUDNICK, I. 1984 Observation of a nonpropagating hydrodynamic soliton. Phys. Rev. Lett. 52, 1421-1425.
39. ZHANG, W. & VIÑALS, J. 1996 Square patterns and quasipatterns in weakly damped Faraday waves. Phys. Rev. E 53, 4283-4286.
40. ZHANG, W. & VIÑALS, J. 1997 Pattern formation in weakly damped parametric surface waves. J. Fluid Mech. 336, 301-330.