Abstract
In the Faraday experiment waves on the surface of a fluid layer are excited by a vertical vibration of the vessel. By virtue of its simplicity this system is outstanding among the pattern forming hydrodynamic systems. The variety of observed ordered patterns is extremely rich and ranges from simple lines to complicated quasi-periodic structures. The aim of this review article is to provide an introduction into the field of Faraday waves, as well as to give an account of the developments during the last decade. Within this period three major lines of interest can be identified: (i) the linear stability theory for viscous fluids, (ii) the interaction of a few spatial degrees of freedom in confined geometries giving way to chaos, and (iii) the formation of well ordered surface patterns in extended geometries and their transition towards spatio-temporal disorder. Special emphasis in this article is placed upon a comparison between theory and experiment.
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References
J. Bechhoefer, V. Ego, S. Manneville, and B. Johnson, J. Fluid Mech. 288, 325 (1995).
T. B. Benjamin and P. Ursell, Proc. R. Soc. Lond. A 225, 505 (1954).
T. Besson, W. S. Edwards, and L.S. Tuckerman, Phys. Rev. E 54, 507 (1996).
M. Bestehorn and R. Friedrich, in J. Parisi, S. C. Müller, W. Zimmermann (eds.), A Perspective Look at Nonlinear Media in Physics, Chemistry and Biology, Springer-Verlag, Berlin (1997).
J. Beyer and R. Friedrich, Phys. Rev. E 51, 1162 (1995).
D. Binks and W. van de Water, Phys. Rev. Lett. 78, 4043 (1997).
E. Bosch, H. Lambermont, and W. van de Water, Phys. Rev. E 49, R3580 (1994).
E. Bosch and W. van de Water, Phys. Rev. Lett. 70, 3420 (1993).
E. Cerda and E. Tirapegui, Phys. Rev. Lett. 78, 859 (1997).
P. Chen and J. Vinals, Phys. Rev. Lett. 79, 2670 (1997).
P. Chen and J. Viñals, J. Fluid Mech. (1998), to appear.
B. Christiansen, P. Alstrøm, and M. T. Levinsen, Phys. Rev. Lett. 68, 2157 (1992).
B. Christiansen, P. Alstrøm, and M. T. Levinsen, J. Fluid Mech. 291, 323 (1995).
S. Ciliberto and J. P. Gollub, Phys. Rev. Lett. 52, 922 (1984).
S. Ciliberto and J. P. Gollub, J. Fluid Mech. 158, 381 (1985).
J. D. Crawford, E. Knobloch, H. Riecke, Physica D 44, 340 (1990).
J. D. Crawford, J. P. Gollub, D. Lane, Nonlinearity 6, 119 (1993).
M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
L. Daudet, V. Ego, S. Manneville, and J. Bechhoefer, Europhys. Lett. 32, 313 (1995).
S. Douady, J. Fluid Mech. 221, 383 (1990).
S. Douady, S. Fauve, and O. Thual, Europhys. Lett. 10, 309 (1989).
W. S. Edwards and S. Fauve, C. R. Acad. Sci. Paris 315-II, 417 (1992).
W. S. Edwards and S. Fauve, Phys. Rev. E 47, R788 (1993).
W. S. Edwards and S. Fauve, J. Fluid Mech. 278, 123 (1994).
A. B. Ezersky, M. I. Rabinovich, V. P. Reutov, and I. M. Starobinets, Sov. Phys. JETP 64, 1228 (1986).
M. Faraday, Philos. Trans. R. Soc. London 52, 319 (1831).
S. Fauve, K. Kumar, C. Laroche, D. Beyens, and Y. Garrabos, Phys. Rev. Lett. 68, 3160 (1992).
B. J. Gluckman, C. B. Arnold, and J. P. GoUub, Phys. Rev. E 51, 1128 (1995).
B. J. Gluckman, P. Marcq, J. Bridger, and J. P. Gollub, Phys. Rev. Lett. 71, 2034 (1993).
H. Haken, Synergetics. An Introduction, 3rd ed., Springer-Verlag, Berlin (1983); H. Haken, Advanced Synergetics, 2nd ed., Springer-Verlag, Berlin (1987).
S. V. Kiyashko, L. N. Korzinov, M. I. Rabinovich, and L. S. Tsimring, Proc. Rev. E 54, 1113 (1996).
A. Kudrolli and J. P. Gollub, Physica D 97, 133 (1996).
A. Kudrolli, B. Pier, and J. P. Gollub, Physica D (1998), to appear.
K. Kumar, Proc. R. Soc. London A 452, 1113 (1996).
K. Kumar and K. Bajaj, Phys. Rev. E 52, R4606 (1995).
K. Kumar and L. Tuckerman, J. Fluid Mech. 279, 49 (1994).
L. Landau and E. M. Lifshitz, Fluid Mechanics, 2nd edn. Pergamon Press (1987).
R. Lifshitz and D. M. Petrich, Phys. Rev. Lett. 79, 1261 (1997).
O. Lioubashevski, J. Fineberg, and L. S. Tuckerman, Phys. Rev. E 55, R3832 (1997).
T. Lundgren and N. Mansour, J. Fluid Mech. 194, 479 (1988).
B. A. Malomed, A. A. Nepomnyashchii, and M. I. Tribelskii, Sov. Phys. LETP 69, 388 (1989).
E. Meron and I. Procaccia, Phys. Rev. A 34, 3221 (1986).
J. W. Miles, Proc. Roy. Soc. Lond. A 297, 459 (1967).
J. Miles and D. Henderson, Ann. Rev. Fluid Mech. 22, 143 (1990).
S. T. Milner, J. Fluid Mech. 225, 81 (1991).
H. W. Müller, Phys. Rev. Lett. 71, 3287 (1993a).
H. W. Müller, Phys. Rev. E 49, 1273 (1993b).
H. W. Müller, H. Wittmer, C. Wagner, J. Albers, and K. Knorr, Phys. Rev. Lett. 78, 2357 (1997).
H. W. Müller, in J. Parisi, S. C. Müller, W. Zimmermann (eds.), A Perspective Look at Nonlinear Media-From Physics to Biology and Social Sciences, Springer-Verlag, Berlin (1998).
A. H. Nayfeh and D. T. Mook, Nonlinear oscillations, Wiley (1979).
M. Neufeld and R. Friedrich, Ann. Phys. Fr. 19, 721 (1994).
M. Neufeld and R. Friedrich, Phys. Rev. E 51, 2033 (1995).
A. C. Newell and Y. Pomeau, J. Physique A 26, L429 (1993).
A. C. Newell and J. A. Whitehead, J. Fluid Mech. 38, 278 (1969).
F. Simonelli and J. P. Gollub, J. Fluid Mech. 199, 471 (1989).
Lord Rayleigh, Phil. Mag. 16, 50 (1883).
K. Ruvinsky, F. Feldstein, and G. Freidman, J. Fluid Mech. 230, 339 (1991).
M. Silber and M. R. E. Proctor, preprint (1977).
J. B. Swift and P. C. Hohenberg, Phys. Rev. A 15, 319 (1977).
N. B. Tufillaro, R. Ramshankar, and J. P. Gollub, Phys. Rev. Lett. 62, 422 (1989).
C. Uhl, R. Friedrich, and H. Haken, Phys. Rev. E 51, 3890 (1995).
M. Umeki and T. Kambe, J. Phys. Soc. Jpn. 58, 140 (1989).
W. Zhang, and J. Viñals, Phys. Rev. Lett. 74, 690 (1995).
W. Zhang and J. Vinals, Phys. Rev. E 53, R4286 (1996).
W. Zhang and J. Vinals, J. Fluid Mech. 336, 301 (1997a).
W. Zhang and J. Vinals, J. Fluid Mech. 341, 225 (1997b).
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Müller, H.W., Friedrich, R., Papathanassiou, D. (1998). Theoretical and Experimental Investigations of the Faraday Instability. In: Evolution of Spontaneous Structures in Dissipative Continuous Systems. Lecture Notes in Physics, vol 55. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49537-1_5
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