关于液体注入的本征正交分解和动态模态分解的物理解释
On the Physical Interpretation of Proper Orthogonal Decomposition and Dynamic Mode Decomposition for Liquid Injection
摘要：
模态分解技术中的本征正交分解（POD）和动态模态分解（DMD）已成为分析动力系统时空相干性的常用方法。特别地，由于多相相互作用的固有复杂性，这些技术对于液体注入系统是感兴趣的，并且期望提取潜在的流动过程。虽然许多研究流动过程的工作已经实现了POD和DMD，但结果往往是高度解释性的，分解理论与所提取模式的解释物理意义之间的联系有限。在这里，我们提供了一个层次结构中的POD和DMD模式的解释的见解。简单的规范系统的模式的解释验证通过知识的基本过程中占主导地位的系统。我们发现，捕获真正的基本现象的模式产生后续模式在高次谐波，直到奈奎斯特极限，其模态结构尺度随模态频率的增加而成比例地降低。这些高次谐波主要对运动信息进行编码，并且可能捕获或可能不捕获附加的结构信息，这取决于系统。我们首先证明了这些研究结果的典型液体喷射系统，以提高解释和理解的结果提取的实际射流在横流系统。
英文摘要：
The modal decomposition techniques of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) have become a common method for analysing the spatio-temporal coherence of dynamical systems. In particular, these techniques are of interest for liquid injection systems due to the inherent complexity of multiphase interactions and extracting the underlying flow processes is desired. Although numerous works investigating flow processes have implemented POD and DMD, the results are often highly interpretive with limited link between the decomposition theory and the interpreted physical meaning of the extracted modes. Here, we provide insight into the interpretation of POD and DMD modes in a hierarchical structure. The interpretation of modes for simple canonical systems is validated through knowledge of the underlying processes which dominate the systems. We show that modes which capture true underlying phenomena produce subsequent modes at higher harmonics, up until the Nyquist limit, whose modal structure scales decrease proportionally with increasing modal frequency. These higher harmonics primarily encode motion information and may or may not capture additional structural information, which is dependent on the system. We demonstrate these findings first on canonical liquid injection systems to enhance the interpretation and understanding of results extracted from practical jet in crossflow systems.
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