EAGER: Network Resilience Analysis of Complex Vortex Interactions

1632003(Taira，Kunihiko)拟议研究的目标是使用为网络理论开发的理论技术来分析复杂的、非稳定的流体流动。本文提出的工作是探索性的，但目的是为研究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。拟议的计算和理论工作将利用网络分析来研究非定常分离流动中存在的基本涡旋相互作用网络及其对扰动的恢复能力。为了实现这项工作的目标，我们将建立适合于连续密集网络表示的流体流动的基于网络的分析技术。流体流动中复杂的非线性相互作用对传统的分析方法提出了挑战，过去还没有得到系统的分析。网络分析在揭示非定常流动中涡旋结构(涡)之间的重要相互联系方面具有很大的潜力。通过了解涡旋网络中哪些相互作用是重要的，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。网络分析的使用将使我们研究流体流动中的涡旋相互作用和能量传递的方式发生革命性的变化。通过建立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。了解涡旋相互作用网络的弹性使我们能够识别敏感的涡旋结构和扰动类型，这些结构和扰动可以以一种补充水动力稳定性分析的方式在全球范围内影响非定常流体流动的动力学。

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.