The Effects of Thermal Noise in a Rayleigh-Benard Cell Near Its First Convective Instability

In recent experiments on the initial stages of pattern formation in a Rayleigh Benard convection cell, Meyer e t al. I1) observed very irregular patterns. In these experiments, the fluid was subjected to a heat current that varied either linearly or periodically in time from below to above the onset of the first instability. If the side wall of the cylindrical cell was made of a material with a thermal diffusivity different from that of the enclosed fluid, a reproducible circular roll pattern was observed at the onset of convection. However, if the thermal diffusivities of side wall and fluid were the same, the pattern at onset was found to be quite irregular and irreproducible. A plausible explanation would be that the onset of patterns is caused by stochastic fluctuations in the currents of heat and momentum. Adding the Landau-Lifshitz expressions for these fluctuations (ref. 2,