Spatial distribution of heat flux and fluctuations in turbulent Rayleigh-B\'enard convection

TL;DR

This study numerically examines how heat flux and fluctuations vary radially in turbulent Rayleigh-Bénard convection, revealing a power-law dependence on Rayleigh number and differences between near-axis and near-wall regions.

Contribution

It provides detailed numerical analysis of radial heat flux distribution and scaling laws in turbulent convection, extending understanding of local heat transport mechanisms.

Findings

Heat flux near the sidewall exceeds that at the center.

Effective power-law scaling of heat flux with Rayleigh number varies radially.

Heat flux near the axis may dominate at very high Rayleigh numbers.

Abstract

We numerically investigate the radial dependence of the velocity and temperature fluctuations and of the time-averaged heat flux $\bar{j}(r)$ in a cylindrical Rayleigh-B\'enard cell with aspect ratio \Gamma=1 for Rayleigh numbers Ra between $2 \times 10^6$ and $2\times 10^{9}$ at a fixed Prandtl number Pr = 5.2. The numerical results reveal that the heat flux close to the sidewall is larger than in the center and that, just as the global heat transport, it has an effective power law dependence on the Rayleigh number, $\bar{j}(r)\propto Ra^{\gamma_j(r)}$. The scaling exponent $\gamma_j(r)$ decreases monotonically from 0.43 near the axis ($r \approx 0$) to 0.29 close to the side walls ($r \approx D/2$). The effective exponents near the axis and the side wall agree well with the measurements of Shang et al. (Phys.\ Rev.\ Lett.\ \textbf{100}, 244503, 2008) and the predictions of Grossmann and Lohse (Phys.\ Fluids \textbf{16}, 1070, 2004). Extrapolating our results to large Rayleigh number would imply a crossover at $Ra\approx 10^{15}$, where the heat flux near the axis would begin to dominate. In addition, we find that the local heat flux is more than twice as high at the location where warm or cold plumes go up or down, than in the plume depleted regions.