### 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.