Pattern formation in two-frequency forced parametric waves.

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.

Two-mode rhomboidal states in driven surface waves

Two-mode rhomboid patterns are generated experimentally via two-frequency parametric forcing of surface waves. These patterns are formed by the simple nonlinear resonance: k-->'2-k-->(2) = k-->(1) where k(1) and k(2)( = k(')(2)) are concurrently excited eigenmodes. The state possesses a direction-dependent time dependence described by a superposition of the two modes, and a dimensionless scaling delineating the state's region of existence is presented. We also show that 2n-fold quasipatterns naturally arise from these states when the coupling angle between k-->(2) and k-->'2 is 2pi/n.

Temporally harmonic oscillons in newtonian fluids

Stationary, highly localized (oscillon) structures are observed in a Newtonian fluid when nonlinear surface waves are parametrically excited with two frequencies. Oscillons have a characteristic structure, that of periodically self-focusing jets. In contrast to previously observed oscillons in highly non-Newtonian media, these states are temporally harmonic with the forcing. For wave amplitudes greater than a critical value, they nucleate from an initial pattern via a hysteretic bifurcation, and can therefore be localized on a background of patterns with a variety of different spatial symmetries.