Plume Fragmentation by Bulk Interactions in Turbulent Rayleigh-Bénard Convection

Using compressed gases with Prandtl numbers near 0.7, we obtained flow visualizations of turbulent Rayleigh-Bénard convection in a cylindrical sample with an aspect ratio $\Gamma \equiv D/L\cong 10$ ($D$ is the diameter and $L$ the height) by the shadowgraph method. Focusing on the plumes under the top plate, we found that their length had a log-normal distribution, suggesting a fragmentation process. Fragmentation events could be visually identified in the images and involved plume interactions with bulk fluctuations or upwelling domain walls. We found the mean spacing between plumes to vary with the Rayleigh number in proportion to the volume-averaged Kolmogorov length of the turbulent bulk fluctuations, providing further evidence for plume-bulk interactions.

Figure 1

Shadowgraph images for ${\mathrm{N}}_2$ and (a) $\mathrm{Ra}=6.8\times {10}^5$, $P=18.62\mathrm{bars}$ and (b) $\mathrm{Ra}=1.1\times {10}^6$, $P=26.20\mathrm{bars}$. The image diameter is equal to 77% of the sample diameter.

Figure 2

Skeletonization of Fig. 1a. (a): Original divided image. (b): Skeletonized plume image. (c): Enlargement of the section in the rectangle in (a) and (b).

Figure 3

Probability distribution $p(l_{\mathrm{pl}}/L)$ of normalized plume lengths $l_{\mathrm{pl}}/L$ for $\mathrm{Ra}=3.4\times {10}^5$ (blue solid squares) and $\mathrm{Ra}=4.3\times {10}^6$ (red solid circles). The lines are fits of Eq. (4) to the data which yielded $a=4.05$, $x_0=0.28$, $\sigma =0.83$ for $\mathrm{Ra}=3.4\times {10}^5$ and $a=12.3$, $x_0=0.22$, $\sigma =0.81$ for $\mathrm{Ra}=4.3\times {10}^6$.

Figure 4

Illustration of fragmentation events for $\mathrm{Ra}=6.8\times {10}^5$. (a): The same image as that in Fig. 1a. (b): An enlargement of the section outlined by a red square in the left image. Red arrows point at fragmentation sites.

Figure 5

Various normalized lengths as a function of Ra. Blue solid circles : Measured mean plume spacing $(A/L_{\mathrm{pl}})/L$ ($0.33\pm 0.03$). Blue open circles: Mean plume spacing $(A/L_{\mathrm{pl}}^{\mathrm{fit}})/L$ based on Eq. (6) ($0.34\pm 0.03$). Purple solid squares: Crossover wavelength $l_{\mathrm{cross}}/L$ of the regions of different exponents of the power spectra (see text) ($0.33\pm 0.03$). Red dashed line: coherence length $l_{\mathrm{coh}}/L=10{\eta }_K/L$ (0.34). Dash-dotted line: $2{\lambda }_b/L=1/\mathrm{Nu}$ (0.28). The number behind each item is the effective exponent from a power-law fit.