Study of dynamics in post-transient flows using Koopman mode decomposition
Study of dynamics in post-transient flows using Koopman mode decomposition
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DOI：
10.1103/physrevfluids.2.124402
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发表时间：
2017-12-29
影响因子：
2.7
通讯作者：
Mezic, Igor
中科院分区：
文献类型：
--
作者：
Arbabi, Hassan;Mezic, Igor
库普曼模式分解（KMD）是一种数据分析技术，通常用于提取复杂流的时空模式。在本文中，我们基于与库普曼算子谱理论相关的定理，使用 KMD 研究二维方形腔中盖驱动流动的动力学。我们采用经典傅立叶和功率谱分析中的两种算法来计算后瞬态流的库普曼算子的离散和连续谱。库夫曼算子谱的属性与 Re = 10 000 和 Re = 30 000 之间发生的流态序列相关，并将流性质从稳定变为非周期性。不同流态（包括具有混合谱的流）的库普曼本征函数是使用状态空间中遍历性的假设构建的。即使流的时间性质发生很大变化，相关的库夫曼模式也显示出显着的鲁棒性。我们观察到，在重建具有强准周期分量的流时，KMD 优于适当的正交分解。
The Koopman mode decomposition (KMD) is a data-analysis technique which is often used to extract the spatiotemporal patterns of complex flows. In this paper, we use KMD to study the dynamics of the lid-driven flow in a two-dimensional square cavity based on theorems related to the spectral theory of the Koopman operator. We adapt two algorithms, from the classical Fourier and power spectral analysis, to compute the discrete and continuous spectrum of the Koopman operator for the post-transient flows. Properties of the Koopman operator spectrum are linked to the sequence of flow regimes occurring between Re = 10 000 and Re = 30 000, and changing the flow nature from steady to aperiodic. The Koopman eigenfunctions for different flow regimes, including flows with mixed spectra, are constructed using the assumption of ergodicity in the state space. The associated Koopman modes show remarkable robustness even as the temporal nature of the flow is changing substantially. We observe that KMD outperforms the proper orthogonal decomposition in reconstruction of the flows with strong quasiperiodic components.