Statistical and geometrical properties of thermal plumes in turbulent Rayleigh-B\'{e}nard convection

TL;DR

This study systematically investigates the geometric and statistical properties of thermal plumes in turbulent Rayleigh-Bénard convection, revealing their shape, scaling laws, and evolution with Rayleigh number through advanced imaging techniques.

Contribution

It provides new insights into the shape, scaling, and evolution of thermal plumes, emphasizing the role of plume number in heat transfer scaling.

Findings

Plumes are rodlike rather than sheetlike.

Plume number density scales with Rayleigh number as Ra^0.3.

Plume area, perimeter, and shape complexity follow log-normal distributions.

Abstract

We present a systematic experimental study of geometric and statistical properties of thermal plumes in turbulent Rayleigh-B\'{e}nard convection using the thermochromic-liquid-crystal (TLC) technique. The experiments were performed in three water-filled cylindrical convection cells with aspect ratios 2, 1, and 0.5 and over the Rayleigh-number range $5\times10^7 \leq Ra \leq 10^{11}$. TLC thermal images of horizontal plane cuts at various depths below the top plate were acquired. Three-dimensional images of thermal plumes were then reconstructed from the two-dimensional slices of the temperature field. The results show that the often-called sheetlike plumes are really one-dimensional structures and may be called rodlike plumes. We find that the number densities for both sheetlike/rodlike and mushroomlike plumes have power-law dependence on $Ra$ with scaling exponents of $\sim 0.3$, which is close to that between the Nusselt number $Nu$ and $Ra$. This result suggests that it is the plume number that primarily d ermines the scaling exponent of the $Nu$-$Ra$ scaling relation. The evolution of the aspect ratio of sheetlike/rodlike plumes reveals that as $Ra$ increases the plume geometry changes from more-elongated to less-elongated. Our study of the plume area fraction (fraction of coverage over the surface of the plate) further reveals that the increased plume numbers with $Ra$ mainly comes from increased plume emission, rather than fragmentation of plumes. In addition, the area, perimeter, and the shape complexity of the two-dimensional horizontal cuts of sheetlike/rodlike plumes were studied and all are found to obey log-normal distributions.