Pattern formation in two-frequency forced parametric waves

H. Arbell and J. Fineberg

The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

Received 24 July 2001; published 5 March 2002

We present an experimental investigation of superlattice patterns generated on the surface of a fluid via parametric forcing with two commensurate frequencies. The spatiotemporal behavior of four qualitatively different types of superlattice patterns is described in detail. These states are generated via a number of different three-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 four-wave interactions that arise when symmetry constraints rule out three-wave resonances.