2016/07/05 by Janet D. Scheel, Jörg Schumacher, Joerg Schumacher · 89 citations
Earth and Planetary Sciences · Engineering · Environmental Science · Mathematics · Physics and Astronomy · #Convection #Fluid Dynamics and Turbulent Flows #Mathematics #Mechanics #Meteorological Phenomena and Simulations #Nusselt number #Physics #Plant Water Relations and Carbon Dynamics #Prandtl number #Reynolds number #Statistical physics #Statistics #Turbulence #Turbulent Prandtl number #physics.flu-dyn
paper · pdf · doi:10.1017/jfm.2016.457
published in Journal of Fluid Mechanics 802, 147-173 (Cambridge University Press)
arxiv created 2016/07/05 · openalex created_date 2016/07/22 · openalex publication_date 2016/08/01 · arxiv updated 2016/09/13 · openalex updated_date 2026/08/05
Statistical properties of turbulent Rayleigh–Bénard convection at low Prandtl numbers Pr , which are typical for liquid metals such as mercury or gallium ( Pr≃ 0.021 ) or liquid sodium ( Pr≃ 0.005 ), are investigated in high-resolution three-dimensional spectral element simulations in a closed cylindrical cell with an aspect ratio of one and are compared to previous turbulent convection simulations in air for Pr=0.7 . We compare the scaling of global momentum and heat transfer. The scaling exponent \unicode[STIX]x1D6FD of the power law Nu=\unicode[STIX]x1D6FCRa^\unicode[STIX]x1D6FD is \unicode[STIX]x1D6FD=0.265± 0.01 for Pr=0.005 and \unicode[STIX]x1D6FD=0.26± 0.01 for Pr=0.021 , which are smaller than that for convection in air ( Pr=0.7 , \unicode[STIX]x1D6FD=0.29± 0.01 ). These exponents are in agreement with experiments. Mean profiles of the root-mean-square velocity as well as the thermal and kinetic energy dissipation rates have growing amplitudes with decreasing Prandtl number, which underlies a more vigorous bulk turbulence in the low- Pr regime. The skin-friction coefficient displays a Reynolds number dependence that is close to that of an isothermal, intermittently turbulent velocity boundary layer. The thermal boundary layer thicknesses are larger as Pr decreases and conversely the velocity boundary layer thicknesses become smaller. We investigate the scaling exponents and find a slight decrease in exponent magnitude for the thermal boundary layer thickness as Pr decreases, but find the opposite case for the velocity boundary layer thickness scaling. A growing area fraction of turbulent patches close to the heating and cooling plates can be detected by exceeding a locally defined shear Reynolds number threshold. This area fraction is larger for lower Pr at the same Ra , but the scaling exponent of its growth with Rayleigh number is reduced. Our analysis of the kurtosis of the locally defined shear Reynolds number demonstrates that the intermittency in the boundary layer is significantly increased for the lower Prandtl number and for sufficiently high Rayleigh number compared to convection in air. This complements our previous findings of enhanced bulk intermittency in low-Prandtl-number convection.