Shevkar Prafulla P, Samuel Roshan J, Zinchenko Georgy, Bode Mathis, Schumacher Jörg, Sreenivasan Katepalli R
Institut für Thermo- und Fluiddynamik, Department of Mechanical Engineering, Ilmenau D-98684, Germany.
Jülich Supercomputing Centre, Forschungszentrum Jülich GmbH, Jülich D-52425, Germany.
Proc Natl Acad Sci U S A. 2025 Aug 12;122(32):e2502972122. doi: 10.1073/pnas.2502972122. Epub 2025 Aug 5.
The link between characteristic coherent structures and their statistical properties in turbulent flows remains largely unclear and is thus a central bottleneck for a better understanding of turbulent flows. Here, we demonstrate this link for the important problem of thermal convection. We show how the hierarchical plume network in the near-wall region of the flow, which becomes increasingly sparse with increasing distance away from the wall, is connected to the marginal stability of the thermal boundary layer and the resulting global heat transport. Our results, which are based on a series of direct numerical simulations for Rayleigh numbers up to [Formula: see text] in a relatively shallow layer, suggest a highly fluctuating thermal boundary layer that is composed of local building blocks in terms of plumes, which are the essential drivers of turbulent heat transport. These thermal plumes are found in a dynamically perpetual process of formation and aggregation that can be described, particularly well for Rayleigh numbers [Formula: see text], by a von Smoluchowski equation resulting in a gamma distribution of the local plume spacing, consistent with measurements. Similarity manifests with respect to the horizontal extension of the network, the vertical hierarchical plume clustering away from the wall and the number of plumes, over an order of magnitude of the thermal boundary layer thickness. Our findings suggest the dominance of dynamical local processes near the wall, rather than a global boundary layer instability.
在湍流中，特征相干结构与其统计特性之间的联系在很大程度上仍不明确，因此是更好地理解湍流的一个核心瓶颈。在此，我们针对热对流这一重要问题展示了这种联系。我们展示了流动近壁区域中层次化的羽流网络是如何与热边界层的边际稳定性以及由此产生的全局热传输相关联的，该羽流网络随着离壁距离的增加而变得越来越稀疏。我们的结果基于在一个相对较浅的层中对高达[公式：见原文]的瑞利数进行的一系列直接数值模拟，表明热边界层高度波动，它由羽流形式的局部构建块组成，而羽流是湍流传热的关键驱动因素。这些热羽流处于一个动态的持续形成和聚集过程中，对于瑞利数[公式：见原文]，这一过程可以特别好地用一个冯·斯莫卢霍夫斯基方程来描述，该方程导致局部羽流间距呈伽马分布，与测量结果一致。在热边界层厚度的一个数量级范围内，网络的水平延伸、远离壁面的垂直层次化羽流聚类以及羽流数量方面都表现出相似性。我们的发现表明壁面附近动态局部过程的主导地位，而非全局边界层不稳定性。
