Shishkina Olga, Wagner Sebastian, Horn Susanne
Institute of Aerodynamics and Flow Technology, German Aerospace Center (DLR), Bunsenstraße 10, 37073 Göttingen, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Mar;89(3):033014. doi: 10.1103/PhysRevE.89.033014. Epub 2014 Mar 21.
We derive the asymptotes for the ratio of the thermal to viscous boundary layer thicknesses for infinite and infinitesimal Prandtl numbers Pr as functions of the angle β between the large-scale circulation and an isothermal heated or cooled surface for the case of turbulent thermal convection with laminar-like boundary layers. For this purpose, we apply the Falkner-Skan ansatz, which is a generalization of the Prandtl-Blasius one to a nonhorizontal free-stream flow above the viscous boundary layer. Based on our direct numerical simulations (DNS) of turbulent Rayleigh-Bénard convection for Pr=0.1, 1, and 10 and moderate Rayleigh numbers up to 108 we evaluate the value of β that is found to be around 0.7π for all investigated cases. Our theoretical predictions for the boundary layer thicknesses for this β and the considered Pr are in good agreement with the DNS results.
对于具有类层流边界层的湍流热对流情况，我们推导了无限和无穷小普朗特数(Pr)下热边界层厚度与粘性边界层厚度之比的渐近线，它是大尺度环流与等温加热或冷却表面之间夹角(\beta)的函数。为此，我们应用了福克纳 - 斯坎假设，它是普朗特 - 布拉修斯假设对粘性边界层上方非水平自由流的推广。基于我们对(Pr = 0.1)、(1)和(10)以及高达(10^8)的中等瑞利数的湍流瑞利 - 贝纳德对流的直接数值模拟（DNS），我们评估了(\beta)的值，发现所有研究案例中该值约为(0.7\pi)。我们针对此(\beta)和所考虑的(Pr)对边界层厚度的理论预测与DNS结果吻合良好。
