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Patterns and quasi-patterns in the Faraday experiment

Published online by Cambridge University Press:  26 April 2006

W. S. Edwards  and
S. Fauve
W. S. Edwards
Affiliation:
Department of Physics, Haverford College, Haverford, PA 19041, USA
S. Fauve
Affiliation:
Laboratoire de Physique, Ecole Normalie Supérieure de Lyon, 46, allée d'Italie, 69364 Lyon Cedex 07, France
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Abstract

Parametric excitation of surface waves via forced vertical oscillation of a container filled with fluid (the Faraday instability) is investigated experimentally in a small-depth large-aspect-ratio system, with a viscous fluid and with two simultaneous forcing frequencies. The asymptotic pattern observed just above the threshold for the first instability of the flat surface is found to depend strongly on the frequency ratio and the amplitudes and phases of the two sinusoidal components of the driving acceleration. Parallel lines, squares, and hexagons are observed. With viscosity 100 cS, these stable standing-wave patterns do not exhibit strong sidewall effects, and are found in containers of various shapes including an irregular shape. A ‘quasi-pattern’ of twelvefold symmetry, analogous to a two-dimensional quasi-crystal, is observed for some even/odd frequency ratios. Many of the experimental phenomena can be modelled via cubic-order amplitude equations derived from symmetry arguments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 278 , 10 November 1994 , pp. 123 - 148
Copyright
© 1994 Cambridge University Press

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