EAGER: Network Resilience Analysis of Complex Vortex Interactions

1632003（Taira，Kunihiko）拟议研究的目的是采用网络理论开发的理论技术分析复杂的非稳态流体流动。本文提出的工作是探索性的，但旨在为检查一系列基本流体流动网络奠定基础，并在未来的研究中纳入不确定性量化，稳定性分析和主动控制技术。所提出的计算和理论工作将使用网络分析来研究非定常分离流中存在的基本涡干扰网络及其对扰动的恢复力。为了实现这项工作的目标，我们将建立基于网络的分析技术，适用于流体流动的连续密集网络表示。流体流动中复杂的非线性相互作用对传统的分析技术提出了挑战，并且在过去没有进行系统的分析。网络分析在揭示非定常流中旋涡结构（涡流）之间的重要联系方面具有很大的潜力。了解了哪些相互作用对涡网络很重要后，图论和网络分析可以为如何描述非定常流体流动的集体动力学提供指导。网络分析的使用将为我们如何研究流体流动中的旋涡相互作用和能量传递提供一个变革性的变化。通过发展流体流动的网络公式，我们可以分析流体网络对扰动和外部强迫输入的弹性。了解涡相互作用网络的弹性，使我们能够识别敏感的涡结构和类型的扰动，可以在全球范围内影响非定常流体流动的动力学，在流体动力学稳定性分析的方式互补。

1632003 (Taira, Kunihiko)The objective of the proposed research is to employ theoretical techniques developed for network theory in the analysis of complex, unsteady fluid flows. The work proposed herein is exploratory in nature but is aimed to lay the foundation for examining a range of fundamental fluid flow networks and to incorporate uncertainty quantification, stability analysis, and active control techniques in future studies. The proposed computational and theoretical work will examine the underlying vortical-interaction networks present in unsteady separated flows and their resilience to perturbations using network analysis. To achieve the goals of this work, we will establish network-based analysis techniques suitable for a continuous dense network representations of fluid flows. Complex nonlinear interactions in fluid flows pose challenges with traditional analysis techniques and have not been systematically analyzed in the past. Network analysis has a great potential for uncovering such important interconnections amongst vortical structures (eddies) in unsteady flows. With knowledge of which interactions are important on the vortical network, graph theory and network analysis can provide guidelines on how to describe the collective dynamics of unsteady fluid flows. The use of network analysis will provide a transformative change to how we examine vortical interactions and energy transfers in fluid flows. By developing the network formulation of fluid flows, we can analyze the resilience of fluid networks against perturbations and external forcing inputs. Understanding the resilience of vortex-interaction networks allows us to identify the sensitive vortical structures and types of disturbances that can globally affect the dynamics of unsteady fluid flows, in a manner complementary to the hydrodynamic stability analysis.