Two-Mode Rhomboidal States in Driven Surface Waves

H. Arbell and J. Fineberg

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

Received 19 May 1999

Two-mode rhomboid patterns are generated experimentally via two-frequency parametric forcing of surface waves. These patterns are formed by the simple nonlinear resonance: k2-k2 = k1 where k1 and k2( = k2) 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 k2 and k2 is 2π/n.