Abstract
A brief review is given of ordered and disordered patterns formed on the surface of a fluid layer subjected to vertical oscillation. We point out connections to cellular BĂ©nard patterns, and discuss the extent of our understanding of these nonlinear states.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Faraday, On a Peculiar Class of Acoustical Figures, and on the Forms of Fluids Vibrating on Elastic Surfaces, Philos. Trans. R. Soc. London 121, 299 (1831).
A. Kudrolli and J.P. Gollub, Patterns and spatiotemporal chaos in parametrically forced surface waves: a systematic survey at large aspect ratio, Physica D 97, 133 (1996).
M.C. Cross and P.C. Hohenberg, Pattern formation outside of equilibrium, Rev. Mod. Phys. 65, 851 (1993).
J. Miles and D. Henderson, Parametrically forced surface waves, Annu. Rev. Fluid Mech. 22, 143 (1990).
A. Kudrolli, B. Pier, and J.P. Gollub, Superlattice Patterns in Surface Waves, Physica D 123, 99 (1998).
T.B. Benjamin and F. Ursell, The stability of the plane free surface of a liquid in vertical periodic motion, Proc. R. Soc. London A 225, 505 (1954).
K. Kumar and L.S. Tuckerman, Parametric instability of the interface between two fluids, J. Fluid Mech. 279, 49 (1994).
J. Bechhoeffer, 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 (1995).
D. Binks and W. van de Water, Nonlinear pattern formation of Fraday waves, Phys. Rev. Lett. 78, 4043 (1997).
P. Chen and J. Viñals, Pattern selection in Faraday waves, Phys. Rev. Lett. 79, 2670 (1997).
W.S. Edwards and S. Fauve, Patterns and quasi-patterns in the Faraday experiment, J. Fluid Mech. 278, 123 (1994).
H. Arbell and J. Fineberg, Two-mode rhomboidal states in driven surface waves, Phys. Rev. Lett. 84, 654 (2000).
M. Silber and M.R.E. Proctor, Nonlinear competition between small and large hexagonal patterns, Phys. Rev. Lett. 81, 2450 (1998).
J. Porter and M. Silber, Broken symmetries and pattern formation in two-frequency forced Farady waves, Phys. Rev. Lett. 89, 084501 (2002).
R. Lifshitz and D.M. Petrich, Theoretical model for Faraday waves with mulitple-frequency forcing, Phys. Rev. Lett. 79, 1261 (1997).
A.B. Ezersky, M.I. Rabinovich, V.P. Reutov, and I.M. Starobinets, Spatiotemporal chaos at parametric excitation of capillary ripples, Zh. Eksp. Teor. Fiz. 91, 2070 (1986).
S.T. Milner, Square patterns and secondary instabilities in driven capillary waves, J. Fluid Mech. 225, 81 (1991).
A. Kudrolli and J.P. Gollub, Localized Spatiotemporal Chaos in Surface Waves, Phys. Rev. E 64, R1052 (1996).
W.B. Wright, R. Budakian, and S.J. Putterman, Diffusing light photography of fully developed isotropic ripple turbulence, Phys. Rev. Lett. 76, 4528 (1996).
F. Melo, P.B. Umbanhowar, and H.L. Swinney, Transition to parametric wave patterns in a vertically oscillated granular layer, Phys. Rev. Lett. 72, 172 (1994).
P.B. Umbanhowar, F. Melo, and H. Swinney, Localized excitaions in a vertically vibrated granular layer, Nature (London) 382, 793 (1996).
O. Lioubashevski, H. Arbell, and J. Fineberg, Dissipative solitary states in driven surface waves, Phys. Rev. Lett. 76, 3959 (1996).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
Gollub, J.P. (2006). Patterns and Chaotic Dynamics in Faraday Surface Waves. In: Mutabazi, I., Wesfreid, J.E., Guyon, E. (eds) Dynamics of Spatio-Temporal Cellular Structures. Springer Tracts in Modern Physics, vol 207. Springer, New York, NY. https://doi.org/10.1007/978-0-387-25111-0_12
Download citation
DOI: https://doi.org/10.1007/978-0-387-25111-0_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-40098-3
Online ISBN: 978-0-387-25111-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)