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.

Diffusive Instabilities and Chemical Reactions

“…The resulting pattern is composed of two discrete but interacting sublattices and thus presents a spatial order on two different length scales. Such dynamic superlattices have also been obtained in nonlinear optical devices [Pampaloni et al, 1997;Musslimani & Pismen, 2000] and in two-frequencies Faraday experiments [Kudrolli et al, 1998;Arbell & Fineberg, 1998]. Finally, for specific relations between the angles of the triads of wave vectors of active modes, quasiperiodic patterns may also be generated.…”

Sideband instabilities and defects of quasipatterns

“…They include superlattices, rhombic states, oscillons, as well as quasipatterns [7][8][9]. In order for superlattices and quasipatterns to be stable the mutual suppression of plane-wave modes of different orientation has to be sufficiently weak.…”

Dynamic Mechanism of Photochemical Induction of Turing Superlattices in the Chlorine Dioxide−Iodine−Malonic Acid Reaction−Diffusion System

“…8,9 In nonequilibrium systems, superlattice patterns are formed by Faraday waves. [10][11][12] They have been found in other hydrodynamic, 13 magnetohydrodynamic, 14 and optical 15 systems. Superlattice patterns are seen on leopard and jaguar skins.…”