Hexagonal and roll flow patterns in temporally modulated Rayleigh-Benard convection

We present experimental results for pattern formation in a thin fluid layer heated time periodically from below. They were obtained with computer-enhanced shadowgraph flow visualization and with heat-flux measurements. The experimental cell was cylindrical, with a radius-to-height ratio of 11.0. The temperature of the top plate was held constant while that of the bottom plate was modulated sinusoidally so that the reduced Rayleigh number ε≡ΔT/ΔTc-1 had the form ε(t)=ε0+δ sin(ωt). Here the time t and frequency ω are scaled by the vertical thermal diffusion time. Experiments were performed within the ranges 8.0≤ω≤18.0, 0.4≤δ≤3.3, and -0.2≤ε0≤0.6. Measurements of the convective threshold shift εc(δ,ω) were in good agreement with theoretical predictions. Comparisons were made with theoretical predictions of a range εA(δ,ω)≤ε0<εR(δ,ω) (εA<εc,εR>εc) where only a hexagonal pattern with downflow at the cell centers is predicted to be stable, a range εR≤ε0<εB(δ,ω) where both hexagonal and roll patterns are expected to be stable, and a range ε0≥εB where only a roll pattern should be stable