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

热对流中湍流上层结构的数值分析：通过拉格朗日聚类和马尔可夫状态建模进行长期动力学

• 批准号: 315181729
• 负责人: Professor Dr. Jörg Schumacher
• 金额: --
• 依托单位: Fachgebiet Strömungsmechanik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/315181729?language=en
• 关键词: Numerical; analysis; turbulent; superstructures; thermal

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.

在水平扩展层中发现了时间平均速度和温度场的大规模模式。这些模式被称为动荡的上层建筑，并将成为本提案的重点。我们想从弱非线性方案中理解它们的动态起源，它们对湍流中不同上层建筑模式之间的湍流热传输和模型过渡的重要性。我们的研究是基于在大型远程比例域中对湍流雷利 - 贝纳德对流的大规模平行的三维直接数值模拟，其中包括非常低和高的prandtl数量。为了回答问题并研究上层建筑的长期演变，我们将不得不减少流量的大量自由度。这是由（1）基于长期低分辨率流量轨迹与短期全分辨率集合模拟的长期低分辨率流轨迹和（2）在拉格朗日示踪轨迹的集合中的（进化）聚类相结合的（1）的广义Markov状态模型完成的。虽然方法（1）给出了不同宏观上层建筑模式之间的过渡概率，但方法（2）揭示了湍流流动中最持久和最长的拉格朗日相干集合。这项工作与流体力学，计算机科学和应用数学的同事一起进行。