标题： 基于亚奈奎斯特率数据的谱本征正交分解 显示英文标题

标题： Spectral proper orthogonal decomposition using sub-Nyquist rate data

摘要： 模态分解方法对于表征复杂系统的低维动力学非常重要，包括湍流。 不同的方法有不同的数据需求，并产生具有不同特性的模态。 谱本征正交分解（SPOD）为统计平稳流动在离散时间频率下生成正交、能量排序的空间模态。 然而，SPOD需要长时间连续、均匀采样的时间解析数据。 这些数据需求限制了SPOD在实验设置中的使用，因为在实验中相机的最大捕获率通常比解析最高湍流频率所需的奈奎斯特采样率要慢。 然而，如果两个PIV系统协同工作，可以获取在时间上任意接近的数据对。 动态模态分解（DMD）利用这些成对的数据来解析高达成对内小时间步长对应的奈奎斯特频率的频率。 然而，这些模态不形成正交基，也没有固定的排序。 本研究尝试从具有小时间步长但成对之间有较大间隙的成对数据中计算SPOD模态。 我们对成对数据使用DMD来估计分段均匀采样的序列，然后可用于估计SPOD模态，旨在解析间隙和成对奈奎斯特极限之间的频率。 该方法在由线性化复Ginzburg-Landau方程得到的数值数据以及马赫数为0.4的等温湍流射流上进行了测试。 对于射流，成对SPOD可以准确去混叠SPOD谱，并在使用超过90%更少数据的情况下，在斯特劳哈尔数St=1.0的频率下估计模态形状。 显示英文摘要

摘要： Modal decomposition methods are important for characterizing the low-dimensional dynamics of complex systems, including turbulent flows. Different methods have varying data requirements and produce modes with different properties. Spectral proper orthogonal decomposition (SPOD) produces orthogonal, energy-ranked spatial modes at discrete temporal frequencies for statistically stationary flows. However, SPOD requires long stretches of sequential, uniformly sampled, time-resolved data. These data requirements limit SPOD's use in experimental settings where the maximum capture rate of a camera is often slower than the Nyquist sampling rate required to resolve the highest turbulent frequencies. However, if two PIV systems operate in tandem, pairs of data can be acquired that are arbitrarily close in time. The dynamic mode decomposition (DMD) uses this pairwise data to resolve frequencies up to the Nyquist frequency associated with the small time step within a pair. However, these modes do not form an orthonormal basis and have no set ranking. The present work attempts to compute SPOD modes from pairwise data with a small time step but with large gaps between pairs. We use DMD on pairwise data to estimate segment-wise, uniformly sampled series that can then be used to estimate the SPOD modes, intending to resolve frequencies between the gap and pair Nyquist limits. The method is tested on numerically obtained data of the linearized complex Ginzburg-Landau equation, as well as a Mach 0.4 isothermal turbulent jet. For the jet, pairwise SPOD can accurately de-alias the SPOD spectrum and estimate mode shapes at frequencies up to St = 1.0 while using over 90% less data.