Spatial and Temporal Dynamics of Two Interacting Modes in Parametrically Driven Surface Waves

Abstract

Nonlinear waves with basic wave numbers, ${k}_{1}$ and ${k}_{2}$, are simultaneously excited via two-frequency parametric excitation of a fluid surface. Three new multiwave states are observed: (1) A superlattice state composed of ${k}_{1}$ and ${k}_{2}$ whose relative orientation is governed by a temporal resonance condition, (2) a superlattice built entirely of wave numbers ${k}_{1}$ and ${k}_{1}/2$, and (3) a state composed of wave numbers of lengths ${k}_{1}$ and ${k}_{2}$ that are uncorrelated in both space and time. The three states exhibit interesting temporal as well as spatial behavior and are observed in a variety of frequency combinations.