Spatially periodic modulated Rayleigh-Bénard convection

Abstract

Two-dimensional thermal convection in a fluid layer between two rigid walls at different mean temperatures is investigated. The top container boundary is undulated and the temperatures at the top and bottom boundaries are spatially periodic modulated, with modulation wavelengths large compared to the thickness of the fluid layer. The continuous translational invariance in the fluid layer is broken by these spatial modulations. Consequently phase differences between two periodic modulations give rise to an interesting drifting pattern, with the drift direction depending on the sign of the relative phase between the modulations. At distinguished ratios between the modulation wave numbers and relative phases the onset of convection changes as function of the modulation amplitudes from a stationary into an oscillatory one: We call this phenomenon Hopf bifurcation by frustrated drifts. Possible experiments are described in detail where this phenomenon can be expected. \textcopyright{} 1996 The American Physical Society.