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

大尺度结构，如涡旋和喷流，通常在地球和天体物理流中观察到。飓风和急流是地球大气中众所周知的例子，但在气体巨星和恒星（如太阳）中也观察到类似的状态。这样的流动几乎总是高度湍流，并显示出大范围的动态活动的时间和空间尺度。此外，它们通常是高度各向异性的，受快速的行星旋转、强分层、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，如细菌悬浮液、精子细胞或其他微游泳者，也会产生类似的由漩涡、射流和强有序状态（如漩涡晶格）组成的流动模式。这些系统属于活性物质的范畴，因为单个游泳者消耗能量来产生流体流动。因此，它们远非统计均衡。具体地说，有人说到主动湍流，尽管重要的是要强调这些流动不是经典意义上的湍流，其特征是小到中等的雷诺数。在非常不同的长度尺度上观察到的现象之间的相似性在形式上反映为两个系统的连续统描述导致相似的方程这一事实。地球和天体物理的湍流通常是由不稳定性产生的，它明确地依赖于不断演变的流动状态。在活动流体中，除了粘性应力外，还有活动应力，它们也显式地（线性地）依赖于流场。在这个项目中，我们在行星和微观尺度上研究复杂流动的自组织。首先，我们考虑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，其中流动是由速度相关的体力产生的。目标是在二维情况下扩展现有的结果，并测试它们对三维扰动的鲁棒性。本课题的第二个主题是该系统的雷诺数依赖性。我们将雷诺数从小到大的数值变化，从而弥合了微观的、积极的模型实现与适用于地球和天体物理极限的高雷诺数流之间的差距。最后，我们还将具体研究这些理想结果在快速旋转的瑞利-巴姆纳德对流中的应用，使用新颖的数值工具来研究该系统中出现的大尺度结构，即漩涡和射流。我们还将这些研究扩展到由于湿度和相位变化引起的内部浮力源的情况下，利用最近引入的“rainy - bsamadard”模型。这个项目将对我们对跨物理尺度的自组织的基本理解做出重大贡献。

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.