Numerical analysis of turbulent superstructures in thermal convection: Long-term dynamics by Lagrangian clustering and Markov state modeling

在水平扩展层中发现了湍流对流时平均速度和温度场的大尺度模式。这些模式被称为湍流上层结构，并将成为本提案的重点。我们希望从弱非线性的角度理解它们的动力学起源，它们对湍流热输运的重要性以及湍流中不同上层结构模式之间的模型转换。我们的研究是基于大展宽比域的湍流瑞利-贝纳德对流的大规模平行三维直接数值模拟，包括非常低和高普朗特数的情况。为了回答这些问题和研究上层建筑的长期演变，我们将不得不减少大量的流动自由度。这是通过(1)基于长期低分辨率流动轨迹的广义马尔可夫状态模型与短期全分辨率集合模拟相结合；(2)拉格朗日示踪剂轨迹集合中的（进化）聚类来实现的。方法(1)给出了不同宏观上层建筑模式之间的转移概率，方法(2)揭示了湍流对流中最持久和最长寿的拉格朗日相干集。这项工作是与来自流体力学、计算机科学和应用数学的同事一起进行的。

Large-scale patterns of the time-averaged velocity and temperature fields are found for turbulent convection in a horizontally extended layer. These patterns are termed turbulent superstructures and will be in the focus of the present proposal. We want to understand their dynamical origin from the weakly nonlinear regime, their importance for the turbulent heat transport and model transitions between different superstructure patterns in turbulence. Our investigations are based on massively parallel three-dimensional direct numerical simulations of turbulent Rayleigh-Benard convection in large-aspect-ratio domains that include very low and high Prandtl number cases. In order to answer the questions and to study the long-term evolution of superstructures, we will have to reduce the vast amount of degrees of freedom of the flow. This is done by (1) generalized Markov state models which are based on a long-term low-resolution flow trajectory in combination with short-term full-resolution ensemble simulations and (2) by (evolutionary) clustering in ensembles of Lagrangian tracer tracks. While method (1) gives transition probabilities between different macroscopic superstructure patterns, method (2) reveals the most persistent and longest-living Lagrangian coherent sets in the turbulent convection flow. The work is conducted together with colleagues from Fluid Mechanics, Computer Science and Applied Mathematics.