用于稳定性和预测分析的条件时空POD扩展
Conditional space-time POD extensions for stability and prediction analysis
摘要：
从湍流中关联和提取相干结构是数据驱动模态分解技术的主要目标。条件时空本征正交分解（CPOD）提供了对瞬态动力学的深入了解，以可定制的方式揭示特定流动现象或事件的原因。这项工作利用了时间演变的CPOD模式在一个减少的子空间，导致新的扩展和适应，满足或超过其他分解方法的能力。然而，它表明，随后的应用程序的动态模式分解（DMD）CPOD模式，提供了一个灵活的工具来调查有针对性的流动不稳定性，音调和对流的性质。通过扩展CPOD时域导出前一种模式，表明CPOD-DMD能准确地再现谱POD模式。关于后者，多分辨率框架（CPOD-mrDMD）产生一个精致的“因果”稳定性分析，能够诊断的自然强迫机制内的流，以及由此产生的不稳定模式。在单独的应用中，CPOD属性在降阶模型的上下文中被理解，其中具有从与CPOD模式相关的有源传感器导出的极端事件的实时流预测的示例。本工作中的各种CPOD功能和观点在以下方面得到了演示：非线性混沌洛伦兹系统、超声速边界层转捩中的3D间歇湍流斑、未启动入口嗡嗡声的纹影视频处理、共振冲击射流的气动声学反馈强迫以及冲击通道壁的间歇性钝体尾流结构的预测。
英文摘要：
The correlation and extraction of coherent structures from a turbulent flow is a principle objective of data-driven modal decomposition techniques. The Conditional space-time Proper Orthogonal Decomposition (CPOD) offers insight into transient dynamics, revealing the causation of specific flow phenomenon - or events, in a customizable manner. This work exploits the temporal evolution of CPOD modes in a reduced subspace, resulting in new extensions and adaptations that meet or exceed the capabilities of other decomposition methods. Chiefly, it is demonstrated that the subsequent application of dynamic mode decomposition (DMD) to CPOD modes, provides a flexible tool to investigate targeted flow instabilities, both tonal and convective in nature. By extending the CPOD time-horizon to educe the former type, it is shown that CPOD-DMD can exactly reproduce Spectral POD modes. Regarding the latter, a multi-resolution framework (CPOD-mrDMD) yields a refined "cause and effect" stability analysis, capable of diagnosing the natural forcing mechanisms within the flow, and the resulting unstable modes. In a separate application, CPOD properties are appreciated in the context of reduced order models, with an example of real-time flow prediction of extreme events derived from an active sensor correlated to a CPOD mode. The various CPOD functions and perspectives in this work are demonstrated on: the nonlinear chaotic Lorenz system, 3D intermittent turbulent spots in supersonic boundary layer transition, Schlieren video processing of unstarted inlet buzz, the aeroacoustic feedback forcing of a resonating impinging jet, and prediction of intermittent bluff-body wake structures impinging on a channel wall.
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