Statistical studies of one-dimensional spatiotemporal chaos in the printer's instability

Abstract

A number of statistical techniques are used to study spatiotemporal chaos in a one-dimensional pattern of fingers which form at a driven oil-air meniscus. It is shown that the long time average of the chaotic pattern is structureless. The rms deviation between finite and infinite time averages decreases approximately as a power law in the averaging time. The results suggest that for short averaging times (i.e., less than about 50 s) the short time average approaches the long time average much like a Gaussian variable, but that for longer averaging times the approach to the infinite-time average is significantly slower than that of a simple Gaussian process. Generally, the early time behavior of the cross-correlation coefficient between patterns recorded at different times decays exponentially around the threshold of STC. The spatial autocorrelation function of the chaotic pattern has a decaying oscillatory tail that is approximately the product of a cosine and a decaying exponential. The correlation length is about equal to the wavelength of the basic pattern.