A. Kudrolli et Jp. Gollub, PATTERNS AND SPATIOTEMPORAL CHAOS IN PARAMETRICALLY FORCED SURFACE-WAVES - A SYSTEMATIC SURVEY AT LARGE ASPECT RATIO, Physica. D, 97(1-3), 1996, pp. 133-154
A systematic experimental survey of both the primary patterns and the
secondary instabilities of parametrically forced surface waves (Farada
y waves) in the large system limit is presented. The symmetry of the p
rimary pattern (stripes, squares, or hexagons) depends on viscosity v
and driving frequency f(0). Hexagons are observed at low f(0) 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 pi (with respect to the forcing). Patterns of different symme
try coexist in certain parameter ranges. The transition to spatiotempo
ral chaos (STC) depends on the symmetry of the primary patterns. The h
exagonal patterns undergo an order/disorder transition in which the an
gular anisotropy in Fourier space declines continuously to zero, Strip
ed 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 wi
th 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.