[论文解读] Modal Isolation and Physics Revelation of a Subcritical Free-Shear Flow by the Dynamic Mode Decomposition

Cruz Y. Li, K.T. Tse+2 more|arXiv (Cornell University)|Oct 13, 2021

Fluid Dynamics and Vibration Analysis参考文献 41被引用 5

一句话总结

本研究将动态模态分解（DMD）应用于方形棱柱上的亚临界自由剪切流，以分离并解释主导的流场结构。DMD成功地将复杂且非线性的流场分解为具有物理解释意义的模态，揭示了诸如斯特劳哈尔涡卷起、开尔文-赫姆霍兹不稳定性、湍流分离泡动力学以及谐波相互作用等机制，具有高度的形态与物理保真度。

ABSTRACT

When analyzing nonlinear systems, it may be the interest of many to isolate individual mechanisms from an amalgam of activities that one often derives from direct observations. The Dynamic Mode Decomposition (DMD) is a novel, Koopman-based technique that potentially offers such functionality. Considering its short history, many aspects of the technique remain unexplored. In this work, we study the modal and physical implications of DMD modes through perhaps one of the most prototypical nonlinear systems: the field of a subcritical free-shear flow over a square prism. We analyzed the ten dominant modes by consulting the flow's mechanics and phenomenology. The results showed that the reduced-order description is morphologically accurate and physically meaningful, successfully decomposing the intertangled nonlinear field into discernible constituents. Mode 1 renders the mean-field. Modes 2 depicts the roll-up of the Strouhal vortex. Mode 3 delineates the Bloor-Gerrard vortex resulting from the Kelvin-Helmholtz instability inside shear layers, its superposition onto the Strouhal vortex, and the concurrent flow entrainment. Modes 4, 5, 7, 8, and 9 portray the harmonics of Modes 2 and 3. Modes 6 and 10 describe the low-frequency shedding of turbulent separation bubbles (TSBs), which contribute to the beating phenomenon in the lift time history and the flapping motion of shear layers. Finally, this work demonstrates the capability of the DMD in providing insights into similar fluid problems. It also serves as a worthy reference for an array of other nonlinear systems.

研究动机与目标

• 利用DMD分离并解释复杂非线性流体系统中的个体流动机制。
• 验证DMD模态在典型亚临界自由剪切流中的物理解释性。
• 确立DMD作为分解交织流动现象为可辨识、具有物理解释意义组分的可靠工具。
• 展示DMD在揭示超越单纯数据分解的深层物理机制方面的能力。

提出的方法

• 将动态模态分解（DMD）应用于方形棱柱上亚临界自由剪切流的快照数据。
• 从时间分辨的流场数据中识别出十个主导DMD模态。
• 通过参照已知的流体力学原理和流动现象，对每个模态进行物理解释。
• 将DMD模态与已知不稳定性相关联：斯特劳哈尔涡旋脱落、开尔文-赫姆霍兹不稳定性以及湍流分离泡。
• 利用模态叠加与谐波分析，识别模态之间的关系。
• 通过与已知流动行为及观测现象（如升力脉动与剪切层振荡）的对比，验证DMD结果。

实验结果

研究问题

• RQ1 DMD能否有效分离并解释非线性、亚临界自由剪切流中的主导流场结构？
• RQ2 流场中各个DMD模态代表了哪些物理机制？
• RQ3 DMD模态如何与涡旋卷起和开尔文-赫姆霍兹不稳定性等已知流体力学现象相关联？
• RQ4 DMD模态在多大程度上捕捉了如湍流分离泡脱落等低频动力学？
• RQ5 DMD能否提供复杂交织流动现象的物理解释性、降阶描述？

主要发现

• 模态1准确代表了平均流场，证实了DMD捕捉基线流场结构的能力。
• 模态2对应于斯特劳哈尔涡卷起，与钝体流中观察到的周期性涡旋脱落一致。
• 模态3捕捉了布罗尔-杰拉德涡旋，即开尔文-赫姆霍兹不稳定性的结果，包括其与斯特劳哈尔涡旋的叠加以及伴随的流体卷吸效应。
• 模态4、5、7、8和9被识别为模态2和3的谐波，表明存在非线性耦合与频率锁定动力学。
• 模态6和10代表低频湍流分离泡（TSB）脱落，其贡献于升力时间历史中的拍频现象。
• DMD分解成功通过相干且具有物理解释意义的模态揭示了剪切层的振荡运动。