Shaking the surface of a fluid layer up and down can cause the formation of Faraday waves. The spatial symmetry of these wave patterns depend on the frequency of forcing. Appropriate design of the forcing function ma lead to the control of the pattern formation.

Abstract:

Faraday waves, of startling beauty and complexity, may form on the surface of a fluid layer when it is shaken up and down. The spatial symmetries of these intricate wave patterns depend on the frequency content of the forcing function in subtle ways that we have tried to illuminate. This in turn suggests ways to control the pattern formation process by an appropriate design of the forcing function. Our analysis is based in equivariant bifurcation theory, while the problems are motivated by laboratory experiments; both will be described.

Keywords:

Faraday waves; Pattern formation; Symmetry.

Lecture #13233

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