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Repeated transients of weakly nonlinear traveling-wave convection.

I present experimental observations of weakly nonlinear traveling-wave convection in ethanol-water mixtures in a narrow, rectangular cell of variable aspect ratio. Over ranges in aspect ratio separated by approximately unity, the first nonlinear state seen above the onset of convection consists of irregular ``repeated transients,'' in which small-amplitude traveling waves initially grow with no change in spatial profile, then lose stability, and finally collapse back down to small amplitude. These states differ qualitatively from the ``blinking'' states seen just above onset at other aspect ratios, in which wave amplitude alternates regularly back and forth across the cell. The collapse in the ``repeated-transient'' state appears to be caused by a dephasing of the pattern which is due to the nonlinear dependence of wave number on amplitude. This dephasing shifts the pattern off resonance, causing its decay.