Self-organization and transitions in anisotropic turbulence: from geophysical to bacterial scales

各向异性湍流的自组织和转变：从地球物理尺度到细菌尺度

• 批准号: 522026592
• 负责人: Dr. Adrian van Kan
• 金额: --
• 依托单位: Department of Physics
• 依托单位国家: 德国
• 项目类别: WBP Fellowship
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/522026592?language=en
• 关键词: Self; organization; transitions; anisotropic; turbulence

Large-scale structures, such as vortices and jets are typically observed in geo- and astrophysical flows. Hurricanes and the Jet Stream are well known examples from Earth's atmosphere, but similar states are also observed on the gas giants and in stars, such as the Sun. Such flows are almost always highly turbulent, and display a wide range of dynamically active temporal and spatial scales. In addition, they are typically highly anisotropic, being subject to rapid planetary rotation, strong stratification, magnetic fields, or thin-layer geometries. On much smaller length scales, biological systems such as suspensions of bacteria, sperm cells, or other microswimmers, create similar flow patterns consisting of vortices, jets and strongly ordered states such as vortex lattices. These systems belong to the category of active matter, since individual swimmers consume energy to create fluid flow. Hence they are far from statistical equilibrium. Specifically, one speaks of active turbulence, although it is important to stress that these flows are not turbulent in the classical sense, being characterised by small to moderate Reynolds numbers. The similarity between the observed phenomena on very disparate length scales is formally reflected by the fact that the continuum descriptipn of both systems leads to similar equations. Geo- and astrophysical turbulence is typically born from instabilities, which explicitly depend on the evolving flow state. In active fluids, there are active stresses, in addition to viscious ones, which also depend explicitly (linearly) on the flow field. In this project, we study the self-organization of complex flows, at planetary, but also microscopic scales. First, we consider an idealized model of strongly anisotropic turbulence driven by instabilities. We consider two-dimensional flows, as well as thin three-dimensional fluid layers, where flow is created by a velocity-dependent body force. The goal is to extend existing results on the two-dimensional case, and to test their robustness with respect to three-dimensional perturbations. The second topic of this project is the Reynolds number dependence of this system. We vary the Reynolds number from small to large values, thus bridging the gap between the microscopic, active realization of the model, and the high-Reynolds number flow that applies to the geo- and astrophysical limit. Finally, we will also study specifically the application of these idealized results to rapidly rotating Rayleigh-Bénard convection, using novel numerically tools to study the emergence of large-scale structures, i.e. vortices and jets in this system. We also extend these investigations to the case of internal buoyancy sources due to moisture and phase changes, utilizing the recently introduced "Rainy-Bénard" model. This project will make a significant contribution to our fundamental understanding of self-organization across physical scales.

大尺度结构，如旋涡和喷流通常在地球和天体物理流动中观察到。飓风和喷流是地球大气层中众所周知的例子，但在气体巨星和恒星（如太阳）中也观察到类似的状态。这种流动几乎总是高度湍流，并显示出广泛的动态活跃的时间和空间尺度。此外，它们通常是高度各向异性的，受到快速行星旋转，强烈分层，磁场或薄层几何形状的影响。在更小的长度尺度上，生物系统，如细菌、精子细胞或其他微泳者的悬浮液，产生类似的流动模式，包括漩涡、射流和强有序状态，如漩涡晶格。这些系统属于活性物质的范畴，因为个体游泳者消耗能量来产生流体流动。因此，它们远远没有达到统计平衡。具体来说，人们谈到了主动湍流，尽管重要的是要强调这些流动不是经典意义上的湍流，其特征在于小到中等的雷诺数。在非常不同的长度尺度上观察到的现象之间的相似性正式反映在这两个系统的连续谱导致类似方程的事实上。地球和天体物理学湍流通常产生于不稳定性，而不稳定性明显取决于不断变化的流动状态。在主动流体中，除了粘性应力之外，还有主动应力，其也明确地（线性地）依赖于流场。在这个项目中，我们研究复杂流动的自组织，在行星，但也微观尺度。首先，我们考虑一个由不稳定性驱动的强各向异性湍流的理想模型。我们考虑二维流动，以及薄的三维流体层，其中流动是由速度依赖的体力。我们的目标是扩展现有的结果在二维的情况下，并测试其鲁棒性相对于三维扰动。该项目的第二个主题是该系统的雷诺数依赖性。我们改变雷诺数从小到大的值，从而弥合之间的差距，微观，积极实现的模型，高雷诺数流动，适用于地理和天体物理极限的差距。最后，我们还将专门研究这些理想化的结果，快速旋转瑞利-贝纳德对流的应用，使用新的数值工具来研究大尺度结构的出现，即在这个系统中的涡和射流。我们还扩展这些调查的情况下，由于水分和相变的内部浮力源，利用最近推出的“Rainy-Bénard”模型。这个项目将为我们对跨物理尺度的自组织的基本理解做出重大贡献。