A statistical model is developed to reconstruct space–time energy spectra in turbulent flows from a non-extensive dataset comprising a time series of velocity fluctuations at a finite number of measurement points. This model is based on a higher approximation of energetic flow structures and developed by using local modulated waves. As a result, it can correctly predict the mean wavenumbers and spectral bandwidths. In contrast, Taylor’s frozen-flow hypothesis incorrectly predicts the spectral bandwidths to be zero, and the local wavenumber model significantly under-predicts the spectral bandwidths. An analytical example is formulated to illustrate the present model, and datasets from direct numerical simulations of turbulent channel flows are used to validate this model. The present statistical model is also discussed in terms of the dominating processes of temporal decorrelation in turbulent flows.

中文翻译：

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用于重建湍流中时空能谱的局部调制波模型

开发了一种统计模型，用于从非广泛数据集重建湍流中的时空能谱，该数据集包括有限数量测量点处速度波动的时间序列。该模型基于能量流结构的更高近似值，并通过使用局部调制波开发。因此，它可以正确预测平均波数和光谱带宽。相比之下，泰勒的冻结流假设错误地预测光谱带宽为零，并且局部波数模型显着低估了光谱带宽。制定了一个分析示例来说明本模型，并使用来自湍流通道流的直接数值模拟的数据集来验证该模型。