Pattern formation in 2-frequency forced parametric waves
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.
Cite
@article{arxiv.nlin/0107072,
title = {Pattern formation in 2-frequency forced parametric waves},
author = {H. Arbell and J. Fineberg},
journal= {arXiv preprint arXiv:nlin/0107072},
year = {2009}
}
Comments
The paper contains 34 pages and 53 figures and provides an extensive review of both the theoretical and experimental work peformed in this system