Statistics of temperature and thermal energy dissipation rate in low-Prandtl number turbulent thermal convection

TL;DR

This study investigates the statistical properties of temperature and thermal energy dissipation in low-Prandtl number turbulent convection, revealing unique scaling laws and distribution characteristics distinct from moderate-Prandtl fluids.

Contribution

It provides new insights into the scaling behavior and distribution of thermal dissipation rates in low-Prandtl number convection through high-resolution simulations.

Findings

Scaling exponents for heat transport and momentum are smaller than in moderate-Prandtl fluids.

Temperature PDFs show stretched exponential peaks and Gaussian tails in the center.

Boundary layer thermal dissipation exceeds bulk dissipation despite smaller volume.

Abstract

We report the statistical properties of temperature and thermal energy dissipation rate in low-Prandtl number turbulent Rayleigh-B\'enard convection. High resolution two-dimensional direct numerical simulations were carried out for the Rayleigh number ($Ra$) of $10^{6} \le Ra \le 10^{7}$ and the Prandtl number ($Pr$) of 0.025. Our results show that the global heat transport and momentum scaling in terms of Nusselt number ($Nu$) and Reynolds number ($Re$) are $Nu=0.21Ra^{0.25}$ and $Re=6.11Ra^{0.50}$, respectively, indicating that the scaling exponents are smaller than those for moderate-Prandtl number fluids (such as water or air) in the same convection cell. In the central region of the cell, probability density functions (PDFs) of temperature profiles show stretched exponential peak and the Gaussian tail; in the sidewall region, PDFs of temperature profiles show a multimodal distribution at relative lower $Ra$, while they approach the Gaussian profile at relative higher $Ra$. We split the energy dissipation rate into contributions from bulk and boundary layers and found the locally averaged thermal energy dissipation rate from the boundary layer region is an order of magnitude larger than that from the bulk region. Even if the much smaller volume occupied by the boundary layer region is considered, the globally averaged thermal energy dissipation rate from the boundary layer region is still larger than that from the bulk region. We further numerically determined the scaling exponents of globally averaged thermal energy dissipation rates as functions of $Ra$ and $Re$.