Statistical studies of chaotic wave patterns

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Abstract
We present statistical measurements of spatially and temporally chaotic surface waves in relatively large containers (10–30 wavelengths across) with various boundary geometries and wetting conditions. The patterns are measured using transmission optics and video image processing. Although the instantaneous patterns are highly disordered, they retain sufficient phase coherence that the time-averaged images have spatially periodic structure. The symmetry of the time-averaged images is related to the symmetry of the boundaries. The convergence of the averaging process is significantly slower than that of a Gaussian random process. An average image can be explained as arising from amplitude and phase fluctuations about a base wave pattern. The form of the base pattern is that expected near onset in an infinite system. The amplitude of the average image, which decreases with drive amplitude, is related to the variance of phase fluctuations. Despite the relatively large dimensions, the base pattern is box quantized by the cell walls. Nonhysteretic jumps occur between these states as the drive frequency is varied. Close to the jumps the patterns fluctuate between several quantized states. Some of the statistical methods utilized here could be employed to analyze spatiotemporal chaos in other systems.

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