Space-time energy spectra describe the distribution of energy density over space and timescales, which are fundamental to studying dynamic coupling at spatial and temporal scales and turbulence-generated noise. The present paper develops a dynamic autoregressive (DAR) random forcing model for space-time energy spectra in turbulent shear flows. This model includes the two essential mechanisms of statistical decorrelation: the convection proposed by Taylor's model and the random sweeping proposed by the Kraichnan-Tennekes model. The new development is that DAR random forcing is introduced to represent the random sweeping effect. The resulting model can correctly reproduce the convection velocity and spectral bandwidths, while a white-in-time random forcing model makes erroneous predictions on spectral bandwidths. The DAR model is further combined with linear stochastic estimation (LSE) to reconstruct the near-wall velocity fluctuations of the desired space-time energy spectra. Direct numerical simulation of turbulent channel flows is used to validate the DAR model and evaluate the Werner-Wengle wall model and the LSE approach. Both the wall model and LSE incorrectly estimate the spectral bandwidths.

中文翻译：

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湍流剪切流中时空能谱的随机动力学模型

时空能谱描述了空间和时间尺度上能量密度的分布，这对于研究时空尺度上的动态耦合以及湍流产生的噪声至关重要。本文为湍流剪切流中的时空能谱建立了动态​​自回归（DAR）随机强迫模型。该模型包括统计去相关的两个基本机制：泰勒模型提出的对流和克拉希南-滕纳克斯模型提出的随机扫描。新的发展是引入了DAR随机强制来表示随机扫描效果。最终的模型可以正确地再现对流速度和频谱带宽，而白时随机强迫模型对频谱带宽进行错误的预测。DAR模型进一步与线性随机估计（LSE）结合，以重建所需时空能谱的近壁速度波动。湍流通道流动的直接数值模拟用于验证DAR模型并评估Werner-Wengle壁模型和LSE方法。壁模型和LSE都错误地估计了光谱带宽。