Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently, DMD has been extended to work with more realistic data that is under-resolved either in time or space, or with data collected in the same spatial domain over multiple independent time windows. In this work, we develop an extension to DMD to synthesize globally consistent modes from velocity fields collected independently in multiple partially overlapping spatial domains. We propose a tractable optimization to identify modes that span multiple windows and align their phases to be consistent in the overlapping regions. First, we demonstrate this approach on data from direct numerical simulation, where it is possible to split the data into overlapping domains and benchmark against ground-truth modes. We consider the laminar flow past a cylinder as an example with distinct frequencies, along with the spatially developing mixing layer, which exhibits a frequency spectrum that evolves continuously as the measurement window moves downstream. Next, we analyze experimental velocity fields from PIV in six overlapping domains in the wake of a cross-flow turbine. On the numerical examples, we demonstrate the robustness of this approach to increasing measurement noise and decreasing size of the overlap regions. In all cases, it is possible to obtain a phase-aligned, composite reconstruction of the full time-resolved flow field from the phase-consistent modes over the entire domain.

中文翻译：

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来自多个重叠空间域的相位一致动态模式分解

动态模式分解（DMD）提供了一种从时间分辨的流场数据中提取物理上可解释的空间模式的原理方法，以及这些模式的幅度如何随时间变化的线性模型。最近，DMD已扩展为可处理在时间或空间上未解决的更真实的数据，或与在多个独立时间窗口内在同一空间域中收集的数据一起使用。在这项工作中，我们开发了DMD的扩展，以从在多个部分重叠的空间域中独立收集的速度场合成全局一致模式。我们提出了一种易于处理的优化，以识别跨越多个窗口的模式并将其相位对齐以在重叠区域中保持一致。首先，我们对直接数值模拟中的数据演示这种方法，可以将数据拆分到重叠的域中，并针对真实模式进行基准测试。我们以流过圆柱的层流为例，它们具有不同的频率，以及空间扩展的混合层，该混合层的频谱随着测量窗口向下游移动而不断发展。接下来，我们在横流式涡轮机之后分析了六个重叠域中PIV的实验速度场。在数值示例上，我们证明了这种方法在增加测量噪声和减小重叠区域大小方面的鲁棒性。在所有情况下，都可以从整个域中的相位一致模式中获得完整的时间分辨流场的相位对齐，复合重建。