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，并且通常显示出令人惊讶的大尺度秩序，即使湍流与小尺度波动和混乱，不规则运动有关。这些大尺度结构在湍流波动的存在下是所谓的湍流超结构的一种表现形式。湍流超结构发生在一系列的原型流，包括壁边界和剪切驱动流以及对流。在第一个资助期内，湍流对流一直是我们调查的中心。在我们以前的建议中，我们已经指出，目前缺乏湍流区大尺度流型的预测理论。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和湍流的相互作用，迄今为止还没有得到很好的表征。另一方面，发展一个有效的描述湍流上层结构的理论工具一直缺失。如下文所述，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，我们已经获得了一个详细的了解，在瑞利-贝纳德对流的大尺度流动特征的能量平衡，我们已经开发了一个启发式的降阶模型来阐明大尺度模式形成的小尺度波动的作用。第二个资助期的主要目标是将这些方法联合收割机结合起来，实现湍流对流上层结构的有效描述。作为SPP内部合作研究的一部分，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，我们亦计划在第二个资助期内扩展该计划。在对湍流对流的上层结构有更深入的了解后，我们还计划将我们的研究扩展到更多种类的紊流，包括剪切流紊流、泰勒-库埃特紊流以及管道和槽道流。这样的比较分析将有助于揭示潜在的普遍机制和特征的湍流上层建筑的生成。

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.