Time Dependence in Rayleigh-Bénard Convection with a Variable Cylindrical Geometry

Abstract

Studies of the first time dependence in Rayleigh-B\'enard convection in $^{4}\mathrm{He}$ are reported. The aspect ratio $\ensuremath{\Gamma}$ could be varied continuously. Data at 31 $\ensuremath{\Gamma}$ values with $4<\ensuremath{\Gamma}<13$ show that near onset the first time dependence is always periodic and associated with changes in the heat transport. The dominant periodicity has a nonzero amplitude, $A$, and vanishing frequency at onset. Changes in $A$ with $\ensuremath{\Gamma}$ show wave-number effects. Except for the time dependence, the transition is consistent with predictions for the skew-varicose instability.