Sources and holes in a one-dimensional traveling-wave convection experiment

Abstract

We study dynamical behavior of local structures, such as sources and holes, in traveling-wave patterns in a very long ͑2 m͒ heated wire convection experiment. The sources undergo a transition from stable coherent behavior to erratic behavior when the driving parameter is decreased. This transition, as well as the scaling of the average source width in the erratic regime are both qualitatively and quantitatively in accord with earlier theoretical predictions. We also present results for the holes sent out by the erratic sources. DOI: 10.1103/PhysRevE.67.036305 PACS number͑s͒: 47.20.Bp, 07.05.Kf, 47.20.Dr, 47.54.ϩr Traveling-wave systems play an exceptional role within the field of pattern formation. If the transition to patterns is supercritical ͑forward͒, the dynamics close to threshold should be amenable to a description by the complex Ginzburg-Landau ͑CGL͒ amplitude equation ͓1͔. Theory and experiments are difficult to compare, however, for the following two reasons.͑i͒ Both the CGL model and experimentally observed traveling-wave patterns exhibit an astonishing variety of ordered, disordered, and chaotic dynamics, which can be difficult to characterize or compare.͑ii͒ The dynamics depends, in general, strongly on nonuniversal coefficients ͓2-4͔, but the values of these coefficients are difficult to determine in experiments ͓5-7͔.The study of local structures, such as sources, fronts, and holes, which play an important role in traveling-wave systems ͓1-4,7-12͔, provide a promising route to compare theory and experiment as they partially circumvent these difficulties: their nontrivial behavior often depends only on a subset of the coefficients ͓11͔ and is, in addition, relatively easy to characterize experimentally ͓7-9,12͔.In this paper, we present a successful example of this approach in a heated wire convection experiment ͑Fig. 1͒. This system forms left and right traveling waves that suppress each other; typical states consist of patches of left and right traveling waves separated by sources ͑which send out waves͒ and sinks ͑which have two incoming waves͒ ͓13͔. An earlier theoretical work ͓14͔, which was based on the amplitude equations ͑1͒ and ͑2͒ below, predicts that, essentially due to the transition from an absolute to a convective instability ͓15͔, sources tend to display a diverging width when the driving parameter is lowered beyond a critical value ͓Eq. ͑3͔͒. More recently, it was predicted that just before these stationary sources would diverge, they become unstable and give way to fluctuating sources of finite average width which display highly nontrivial dynamics ͓4͔.We indeed observe this nontrivial change in source behavior when the driving ͑heating of wire͒ is decreased; not only the measured transition value, but also the qualitative behavior of sources is in accord with the predictions ͓14,4͔. All properties necessary to compare theory and experiment are measured in a set of independent experiments. The fluctuating sources send out holes, and we show that these display behavior very simil...

Coherent and incoherent structures in systems described by the 1D CGLE: experiments and identification

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Defects in Oscillatory Media: Toward a Classification

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Amplitude modulation and relaxation-oscillation of counterpropagating rolls within a broken-symmetry laser-induced electroconvection strip

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