大纵横比湍流瑞利-贝纳德对流实验中的拉格朗日粒子与粒子团簇

中文摘要 AI 辅助

我们在纵横比Gamma=10、瑞利数Ra=9.3×10^7、普朗特数Pr=4.8的湍流瑞利-贝纳德对流中开展拉格朗日粒子追踪实验，追踪约5万个中性浮力粒子，时长最长达150个柯尔莫哥洛夫时间。所得轨迹足够长，可捕捉单个粒子从短时间弹道 regime 到长时间扩散 regime 的均方位移。我们进一步分析拉格朗日速度结构函数与粒子对色散，二者在各自时间 regime 中均呈现与理论预期一致的标度行为。在类理查森 regime 中，粒子对色散指数超过3，横向方向表现最为明显。通过主成分分析，我们对初始半径约为8和20个柯尔莫哥洛夫长度的粒子云开展多粒子统计研究，发现粒子云横向方向的扩散强于垂直方向，且在约10个柯尔莫哥洛夫时间内从初始球形变形为扁椭球，呈现明显的各向异性色散。我们通过图拉普拉斯的谱分析结合k-means聚类，从粒子连接网络中识别动力学特征。此外，我们分析三个加速度分量的概率密度函数，并评估其二阶和四阶矩的统计收敛性。横向加速度分量比垂直分量更具间歇性，表现为更重的尾部；而在主体区域条件下的加速度统计，其间歇性略低于整个测量体积范围内的结果，我们将此归因于壁面附近发生的高度间歇性羽流喷射与羽流聚集事件。

英文摘要

We perform Lagrangian particle-tracking experiments in turbulent Rayleigh-Bénard convection at aspect ratio Gamma = 10, Rayleigh number Ra = 9.3 x 10^7, and Prandtl number Pr = 4.8. Approximately 50,000 neutrally buoyant particles are tracked for durations of up to 150 Kolmogorov times. The resulting trajectories are sufficiently long to capture the mean-square displacement of single particles from the short-time ballistic regime to the long-time diffusive regime. We further analyse Lagrangian velocity structure functions and particle-pair dispersion, both of which exhibit scaling behavior consistent with theoretical expectations in their respective temporal regimes. In the Richardson-like regime, the pair-dispersion exponent exceeds 3, most clearly in the lateral direction. Multi-particle statistics are investigated by analysing particle clouds with initial radii of approximately 8 and 20 Kolmogorov lengths using principal component analysis. The clouds spread more strongly in the lateral directions than in the vertical direction and deform from initially spherical shapes into oblate ellipsoids within approximately 10 Kolmogorov times, revealing pronounced anisotropic dispersion. The dynamics is identified from the particle-connectivity network through a spectral analysis of the graph Laplacian followed by k-means clustering. Furthermore, we examine the probability density functions of all three acceleration components and assess the statistical convergence of their second and fourth moments. The lateral acceleration components are more intermittent than the vertical component, as indicated by their heavier tails. Acceleration statistics conditioned on the bulk region are slightly less intermittent than those obtained over the full measurement volume, which we attribute to the highly intermittent plume-ejection and plume-aggregation events occurring near the walls.

发表机构

• Technische Universität Ilmenau（埃尔朗根-纽伦堡工业大学）

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