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

Abstract

We report the statistical properties of temperature and thermal energy dissipation rate in low-Prandtl number turbulent Rayleigh-Bénard convection. High resolution twodimensional direct numerical simulations were carried out for the Rayleigh number (Ra) of 10 6 ≤ Ra ≤ 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. a a) This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Xu et al., Phys. Fluids 31, 125101 (2019) and may be found at

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