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We report the statistical properties of temperature and thermal energydissipation rate in low-Prandtl number turbulent Rayleigh-B\'enard convection.High resolution two-dimensional direct numerical simulations were carried outfor the Rayleigh number ($Ra$) of $10^{6} \le Ra \le 10^{7}$ and the Prandtlnumber ($Pr$) of 0.025. Our results show that the global heat transport andmomentum 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 thatthe 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 ofthe cell, probability density functions (PDFs) of temperature profiles showstretched exponential peak and the Gaussian tail; in the sidewall region, PDFsof temperature profiles show a multimodal distribution at relative lower $Ra$,while they approach the Gaussian profile at relative higher $Ra$. We split theenergy dissipation rate into contributions from bulk and boundary layers andfound the locally averaged thermal energy dissipation rate from the boundarylayer 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 isconsidered, the globally averaged thermal energy dissipation rate from theboundary layer region is still larger than that from the bulk region. Wefurther numerically determined the scaling exponents of globally averagedthermal energy dissipation rates as functions of $Ra$ and $Re$.

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