Effective Description of Superstructures in Turbulent Convection and Simple Turbulent Shear Flows

湍流是自然界中普遍存在的现象，尽管湍流与小规模波动和混沌、不规则运动有关，但它往往表现出令人惊讶的大规模秩序。这些存在湍流起伏的大尺度结构是所谓湍流上层结构的一种表现形式。湍流上层结构出现在一系列的原型流动中，包括壁面流动和剪切驱动流动以及对流流动。在第一个资助期，湍流对流一直是我们研究的中心。在我们之前的建议中，我们已经指出，目前缺乏湍流状态下大规模流动模式的预测理论。一方面，这是由于湍流上层结构的动力学，特别是大尺度流动特征与湍流的相互作用，到目前为止还没有很好地表征。另一方面，发展湍流上层结构有效描述的理论工具一直缺失。如下所述，我们在第一个供资期内就这两项挑战取得了可喜的进展。特别是，我们详细了解了rayleigh - b郁闷对流中大尺度流动特征的能量平衡，并建立了启发式降阶模型来阐明小尺度波动对大尺度模式形成的作用。第二个资助期的主要目标是将这些方法结合起来，以实现对湍流对流上层结构的有效描述。作为SPP合作研究的一部分，我们与Juan Pedro Mellado密切合作，并将我们的理论分析应用于对流大气流动，我们还计划在第二个资助期扩展。在对湍流对流中的上层结构有了更好的了解之后，我们还计划将我们的研究扩展到更多种类的湍流，包括剪切流湍流、Taylor-Couette湍流以及管道和通道流动。这种比较分析将有助于揭示湍流上层建筑产生的潜在普遍机制和特征。

Turbulent flows are a ubiquitous phenomenon in nature and often show a surprising large-scale order, even though turbulence is associated with small-scale fluctuations and chaotic, irregular motion. These large-scale structures in presence of turbulent fluctuations are one manifestation of so-called turbulent superstructures. Turbulent superstructures occur in a range of prototypical flows including wall-bounded and shear-driven flows as well as in convective flows. Turbulent convection has been at the center of our investigations in the first funding period. In our previous proposal we have pointed out that a predictive theory of large-scale flow patterns in the turbulent regime is currently lacking. On the one hand, this is due to the fact that dynamics of turbulent superstructures, and in particular the interaction of large-scale flow features and turbulence, so far was not well characterized. On the other hand, theoretical tools to develop an effective description of turbulent superstructures have been missing. As detailed below, we have made promising progress with respect to both of these challenges in the first funding period. In particular, we have gained a detailed understanding of the energy balance of large-scale flow features in Rayleigh-Bénard convection, and we have developed a heuristic reduced-order model to elucidate the role of small-scale fluctuations on large-scale pattern formation. The primary goal for the second funding period is to combine these approaches to achieve an effective description of superstructures in turbulent convection.As part of the collaborative research within the SPP we have closely collaborated with Juan Pedro Mellado and have applied our theoretical analysis to convective atmospheric flows, which we also plan to extend in the second funding period.Having gained a better understanding of superstructures in turbulent convection, we also plan to extend our investigations to a greater variety of turbulent flows, including shear flow turbulence, Taylor-Couette turbulence as well as pipe and channel flows. Such comparative analyses will help to shed light on potentially universal mechanisms and features in the generation of turbulent superstructures.