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.