## Faraday Waves

Applying a vertical sinusoidal oscillation to a dish of fluid effectively modulates the acceleration of gravity seen by the fluid. If this modulation exceeds a critical value, the normally flat state of the free surface becomes unstable to the formation of surface waves. These waves have a frequency which is half that of the driving oscillations (the first sub-harmonic). This effect was first reported by Michael Faraday in 1831.

In ordinary Newtonian fluids (those that do not exhibit shear thickening or shear thinning) the wave patterns include ones with 1-fold symmetry (stripes), 2-fold symmetry (squares), 3-fold symmetry (hexagons) as well as higher orders of symmetry.

Stripes
Squares
Hexagons

When you quickly pass through onset using a circular dish, spirals and concentric circle patterns can also be produced. These patterns are metastable for about 10 minutes. The center then begins to drift to one side and eventually the stable striped pattern results:

Spiral
Circle

An interesting variation of the Faraday experiment is to place a dry granular material in a dish and subject it to similar vertical oscillations. Many of the same patterns seen in the liquid version of the experiment are also seen in the granular material. In addition, localized structures called "oscillons" have been observed.

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