Temporal or spatial structures are readily extracted from complex data by modal decompositions like proper orthogonal decomposition (POD) or dynamic mode decomposition (DMD). Subspaces of such decompositions serve as reduced order models and define either spatial structures in time or temporal structures in space. On the contrary, convecting phenomena pose a major problem to those decompositions. A structure traveling with a certain group velocity will be perceived as a plethora of modes in time or space, respectively. This manifests itself for example in poorly decaying singular values when using a POD. The poor decay is counterintuitive, since a single structure is expected to be represented by a few modes. The intuition proves to be correct, and we show that in a properly chosen reference frame along the characteristics defined by the group velocity, a POD or DMD reduces moving structures to a few modes, as expected. Beyond serving as a reduced model, the resulting entity can be used to define a constant or minimally changing structure in turbulent flows. This can be interpreted as an empirical counterpart to exact coherent structures. We present the method and its application to a head vortex of a compressible starting jet.

中文翻译：

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一个特征动态模式分解

通过模态分解，如适当的正交分解 (POD) 或动态模态分解 (DMD)，可以很容易地从复杂数据中提取时间或空间结构。这种分解的子空间用作降阶模型并定义时间上的空间结构或空间中的时间结构。相反，对流现象对这些分解构成了主要问题。以特定群速度运行的结构将分别被视为时间或空间中的过多模式。例如，当使用 POD 时，这表现在衰减不佳的奇异值中。较差的衰减是违反直觉的，因为预计单个结构将由几种模式表示。直觉证明是正确的，我们表明，在沿着群速度定义的特征正确选择的参考系中，POD 或 DMD 将移动结构减少到几种模式，正如预期的那样。除了用作简化模型之外，生成的实体还可用于定义湍流中恒定或变化最小的结构。这可以解释为精确相干结构的经验对应物。我们介绍了该方法及其在可压缩起始射流的头部涡流中的应用。