Pattern Competition in Temporally Modulated Rayleigh-Bénard Convection

Shadowgraph flow-visualization studies and heat-flux measurements were used to study convection subjected to temporal modulation of the Rayleigh number $R$ in the form $\epsilon \mathrm{}\left(t\right)=\frac{R\left(t\right)\mathrm{}}{R_c^{\mathrm{stat}}}-1={\epsilon }_0+\delta sin\left(\omega t\right)$, where $R_c^{\mathrm{stat}}$ is the unmodulated threshold, and $\omega$ and $t$ are scaled by the vertical thermal diffusion time. For $\omega =15\mathrm{}$ and $0.7\lesssim \delta \lesssim 2.0$ the predicted hexagonal patterns were observed for a range of ${\epsilon }_0$ immediately above the convective threshold ${\epsilon }_c$. With increasing ${\epsilon }_0$ there is a region exhibiting coexistence between hexagons and rolls, followed by roll-like patterns. The observed boundaries between these regions and the magnitude of the convective heat transport are consistent with theory.