AI 中文总结
研究瑞利-贝纳德对流中速度环流统计特性，通过直接数值模拟，发现热边界层内基本涡旋分布与温度场强相关，核心长宽比统计改变，环流概率分布函数有类似HIT的特征，远离热边界层时结构统计行为也似HIT。
AI 中文摘要
近年来，均匀各向同性湍流（HIT）中速度环流的重要统计特性已被揭示，这引发了它们在其他类湍流中是否持续或被修改的问题。受小尺度结构在HIT环流波动中的主导作用启发，我们在瑞利数为\(10^9\)、普朗特数为\(O(1)\)的瑞利-贝纳德对流直接数值模拟中研究它们的相关性。在热边界层（TBL）内，发现基本涡旋的分布与温度场密切相关，而其核心长宽比的统计显著改变。此外，为平行于壁面的平面轮廓计算的环流概率分布函数显示出与HIT中观察到的显著特征相似，‘面积规则’（环流统计与极小曲面之间的联系）仍然特别满足——除了在几个TBL厚度距离处可能的过渡区域。在远离TBL的地方，正如预期的那样，这些结构的整体统计行为同样类似于HIT，其中小涡管的间歇性空间分布由能量耗散场决定。
英文摘要
Important statistical properties of velocity circulation in homogeneous isotropic turbulence (HIT) have been unveiled in recent years, raising the question of whether they persist, or are modified, in other classes of turbulent flows. Motivated by the dominant role of small-scale structures in the circulation fluctuations of HIT, we investigate their relevance in direct numerical simulations of Rayleigh-Bénard convection at a Rayleigh number of $10^9$ and Prandtl number of $O(1)$. Within the thermal boundary layer (TBL), the distribution of elementary vortices is found to be strongly correlated with the temperature field, while the statistics of their core aspect ratios is significantly altered. Additionally, the probability distribution functions of circulation, computed for planar contours which are parallel to the walls, display salient features closely akin to those observed in HIT, with the {\it Area Rule} (a connection between circulation statistics and minimal surfaces) remaining particularly well satisfied -- except for a possible transitional region at a distance of a few TBL thicknesses. Away from the TBL, as expected, the overall statistical behavior of these structures likewise resembles that of HIT, where the intermittent spatial distribution of small vortex tubes is instead determined by the energy dissipation field.
Comments22 pages, 7 figures
