Stochastic influences on pattern formation in Rayleigh-Bénard convection: Ramping experiments

We report on computer-enhanced shadowgraph flow-visualization and heat-flux measurements of pattern formation in convective flows in a thin fluid layer of depth d that is heated from below. Most of the experiments were conducted in a cylindrical container of radius r and aspect ratio Γ==r/d=10. The temperature of the top plate of the container was held constant while the heat current through the fluid was linearly ramped in time, resulting in a temperature difference ΔT between the bottom and top plates. After initial transients ended, the reduced Rayleigh number ε==ΔT/Δ${\mathit{T}}_{\mathit{c}}$-1, where Δ${\mathit{T}}_{\mathit{c}}$ is the critical temperature difference for the onset of convection, increased linearly with ramp rate β such that ε(t)=βt. When time was scaled by the vertical thermal diffusion time, our ramp rates were in the range 0.01≤β≤0.30. When the sidewalls of the cell were made of conventional plastic materials, a concentric pattern of convection rolls was always induced by dynamic sidewall forcing. When sidewalls were made of a gel that had virtually the same thermal diffusivity as the fluid, pattern formation occurred independent of cell geometry. In the earliest stages the patterns were then composed of irregularly arranged cells and varied randomly between experimental runs. The same random cellular flow was also observed in samples of square horizontal cross section. The results demonstrate the importance of stochastic effects on pattern formation in this system. However, an explanation of the measured convective heat current in terms of theoretical models requires that the noise source in these models have an intensity that is four orders of magnitude larger than that of thermal noise.