Patterns and quasi-patterns in the Faraday experiment

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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.

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