Four different applications of spectral proper orthogonal decomposition (SPOD) are demonstrated on large-eddy simulation data of a turbulent jet. These are: low-rank reconstruction, denoising, frequency–time analysis and prewhitening. We demonstrate SPOD-based flow-field reconstruction using direct inversion of the SPOD algorithm (frequency-domain approach) and propose an alternative approach based on projection of the time series data onto the modes (time-domain approach). We further present a SPOD-based denoising strategy that is based on hard thresholding of the SPOD eigenvalues. The proposed strategy achieves significant noise reduction while facilitating drastic data compression. In contrast to standard methods of frequency–time analysis such as wavelet transform, a proposed SPOD-based approach yields a spectrogram that characterises the temporal evolution of spatially coherent flow structures. A convolution-based strategy is proposed to compute the time-continuous expansion coefficients. When applied to the turbulent jet data, SPOD-based frequency–time analysis reveals that the intermittent occurrence of large-scale coherent structures is directly associated with high-energy events. This work suggests that the time-domain approach is preferable for low-rank reconstruction of individual snapshots, and the frequency-domain approach for denoising and frequency–time analysis.

中文翻译：

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使用 SPOD 对湍流进行频时分析、低秩重构和去噪

在湍流射流的大涡模拟数据上演示了光谱适当正交分解 (SPOD) 的四种不同应用。它们是：低秩重建、去噪、频时分析和预白化。我们使用 SPOD 算法的直接反演（频域方法）演示了基于 SPOD 的流场重建，并提出了一种基于将时间序列数据投影到模式上的替代方法（时域方法）。我们进一步提出了一种基于 SPOD 特征值的硬阈值的基于 SPOD 的去噪策略。所提出的策略实现了显着的降噪，同时促进了剧烈的数据压缩。与频率时间分析的标准方法（如小波变换）相比，提出的基于 SPOD 的方法产生了一个频谱图，该频谱图表征了空间相干流结构的时间演变。提出了一种基于卷积的策略来计算时间连续扩展系数。当应用于湍流射流数据时，基于 SPOD 的频率-时间分析表明，大尺度相干结构的间歇性发生与高能事件直接相关。这项工作表明，时域方法更适用于单个快照的低秩重建，而频域方法更适用于去噪和频时分析。基于 SPOD 的频率-时间分析表明，大尺度相干结构的间歇性发生与高能事件直接相关。这项工作表明，时域方法更适用于单个快照的低秩重建，而频域方法更适用于去噪和频时分析。基于 SPOD 的频率-时间分析表明，大尺度相干结构的间歇性发生与高能事件直接相关。这项工作表明，时域方法更适用于单个快照的低秩重建，而频域方法更适用于去噪和频时分析。