Coherent superstructures in turbulent pipe and Taylor-Couette flows

自然界和工程中的流体运动通常以大规模的相干运动为特征，即所谓的上层结构，它受到边界条件、几何形状和驱动源的强烈影响。湍流上层结构携带着很大一部分动能，它们产生阻力，并且常常支配着整个流体系统的热、质量和动量输运性质。因此，为了超越最先进的湍流建模和控制策略，必须正确地考虑上部结构。在这个项目中，我们将研究两种典型设置下上部结构的动力学、能量学和输运性质：圆柱管流动和两个旋转同心圆柱体之间的Taylor- Couette流动，特别是在窄间隙限制下。首先，我们将确定上层建筑是通过更小尺度的相干排列收集能量，还是直接从平均剪切收集能量。我们将通过使用（空间）滤波方法从直接数值模拟数据中计算尺度间能量通量来实现这一点。其次，为了帮助小组在优先计划中开发特征和检测方法，我们将提供并维护高分辨率的数据集，这些数据集将使用我们的过滤工具自适应地降低空间和时间的复杂性。利用这些方法，我们将研究拉格朗日相干结构与能量通量之间的关系。我们的工作将建立在第一个资助阶段建立的合作网络的基础上，并将允许弥合目前在高雷诺数方面的差距。

Fluid motions in nature and engineering typically feature large-scale coherent motions, so-called superstructures, which are strongly shaped by boundary conditions, geometry and source of driving. Turbulent superstructures carry a substantial part of the kinetic energy, they contribute to drag and they often dominate heat, mass and momentum transport properties of the entire fluid system. Hence, in order to go beyond state-of-the-art modelling and control strategies of turbulent flows, superstructures must be correctly accounted for. In this project, we will investigate the dynamics, energetics and transport properties of superstructures in two canonical setups: cylindrical pipe flow and Taylor--Couette flow between two rotating concentric cylinders, especially in the narrow-gap limit. First, we will determine whether superstructures harvest energy through coherent alignment of much smaller scales, or directly from the mean shear. We will achieve this by computing the inter-scale energy flux from direct numerical simulation data with a (spatially) filtering approach. Second, in order to aid the groups developing characterisation and detection methods within the Priority Programme we will offer and maintain highly-resolved data sets, which will be adaptively reduced in spatial and temporal complexity using our filtering tools. With these methods, we will investigate the relationship between Lagrange coherent structures and energy fluxes. Our work will build upon the network of collaborations established in the first funding phase and will allow bridging the current gap towards high Reynolds numbers.