Patterns and spatiotemporal chaos in parametrically forced surface waves: a systematic survey at large aspect ratio

Abstract

A systematic experimental survey of both the primary patterns and the secondary instabilities of parametrically forced surface waves (Faraday waves) in the large system limit is presented. The symmetry of the primary pattern (stripes, squares, or hexagons) depends on viscosity ν and driving frequency f o . Hexagons are observed at low f o over the whole viscosity range despite the subharmonic symmetry that tends to suppress them. Possible mechanisms for the occurrence of hexagons for single frequency forcing are discussed. Boundary-induced distortion is absent for the hexagonal and square patterns, but present for stripes. Phase defects occur between hexagonal domains differing in temporal phase by π (with respect to the forcing). Patterns of different symmetry coexist in certain parameter ranges. The transition to spatiotemporal chaos (STC) depends on the symmetry of the primary patterns. The hexagonal patterns undergo an order/disorder transition in which the angular anisotropy in Fourier space declines continuously to zero. Striped patterns at high viscosity become unstable via transverse amplitude modulations in regions of high curvature; this instability results in a spatially nonuniform mixed state in which domains of STC coexist with stripes. We propose that this phenomenon may be understood in terms of a critical curvature that depends on the acceleration. A secondary oscillatory instability is also observed to deform the stripes within the mixed state at intermediate viscosities.