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Pattern formation in 2-frequency forced parametric waves

H. Arbell·J. Fineberg
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Abstract

We present an experimental investigation of superlattice patterns generated on the surface of a fluid via parametric forcing with 2 commensurate frequencies. The spatio-temporal behavior of 4 qualitatively different types of superlattice patterns is described in detail. These states are generated via a number of different 3--wave resonant interactions. They occur either as symmetry--breaking bifurcations of hexagonal patterns composed of a single unstable mode or via nonlinear interactions between the two primary unstable modes generated by the two forcing frequencies. A coherent picture of these states together with the phase space in which they appear is presented. In addition, we describe a number of new superlattice states generated by 4--wave interactions that arise when symmetry constraints rule out 3--wave resonances.

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H. Arbell, J. Fineberg. 2001-07-31. Pattern formation in 2-frequency forced parametric waves. https://doi.org/10.1103/physreve.65.036224

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