论文标题
网络广播分析和控制湍流
Network broadcast analysis and control of turbulent flows
论文作者
论文摘要
我们提出了一种基于网络的模态分析技术，该技术识别了关键的动力学路径，扰动会在时间变化的基础流中放大。该分析建立在Katz中心性的基础上，该中心性揭示了可以有效地传播扰动的流动结构，这些流动在基本流程上的涡旋相互作用网络上。由KATZ函数的分解形式的动机，我们采用了所得的可沟通矩阵的奇异值分解，并补充了流体流的分解分析。右灵向量（称为广播模式）可以对敏感区域进行见解，在这些区域中，可以有效地传播和放大引入的扰动，并在整个及时演变的流体流网络上进行扩增。我们将此分析应用于二维衰减各向同性湍流。广播模式表明，涡流偶极子是扩散扰动的重要结构。通过使用主广播模式扰动流量，我们演示了从当前分析中获得的见解的实用性，以有效地修改湍流的演变。当前的网络启发性工作介绍了网络分析的新颖使用，以指导流程控制工作，特别是对于时变基础流。
We present a network-based modal analysis technique that identifies key dynamical paths along which perturbations amplify over a time-varying base flow. This analysis is built upon the Katz centrality, which reveals the flow structures that can effectively spread perturbations over a time-evolving network of vortical interactions on the base flow. Motivated by the resolvent form of the Katz function, we take the singular value decomposition of the resulting communicability matrix, complementing the resolvent analysis for fluid flows. The right-singular vectors, referred to as the broadcast modes, give insights into the sensitive regions where introduced perturbations can be effectively spread and amplified over the entire fluid-flow network that evolves in time. We apply this analysis to a two-dimensional decaying isotropic turbulence. The broadcast mode reveals that vortex dipoles are important structures in spreading perturbations. By perturbing the flow with the principal broadcast mode, we demonstrate the utility of the insights gained from the present analysis to effectively modify the evolution of turbulent flows. The current network-inspired work presents a novel use of network analysis to guide flow control efforts, in particular for time-varying base flows.
