时空能谱是研究湍流中不同时空尺度运动之间耦合作用的基本工具，也在湍流噪声、风能等领域有着广泛的工程应用。为了得到完整的时空能谱，我们需要包含从Kolmogorov尺度到积分尺度的所有尺度的流场数据。这不论对于数值计算还是实验测量而言都是一个巨大的挑战。因此，提出与实验或数值数据相符的速度、压力时空谱模型将是十分有必要的。

在本文中，我们从理论和数值的角度研究了缓冲区速度脉动的时空谱以及壁面压力时空谱。本文的主要成果如下：

1.本文将基于预解算子的时空能谱估计方法(RBE方法)应用于预测槽道湍流中流向速度脉动的均方根(RMS)速度和时空能谱。该方法的输入是对数区中一个平行壁面的参考平面上的速度时空能谱，输出是缓冲区中的速度时空能谱。为了便于数值计算，本文详细给出了RBE方法的离散形式。数值结果表明，RBE方法可以用于预测速度时空能谱的谱宽与对流速度。此外，我们通过改变RBE方法的输入研究了RBE方法对于时空能谱的预测性能。具体而言，我们研究了参考平面法向位置和个数、系统输入中是否包括压力、压力边界条件和窗函数的选取对于预测结果的影响。结果表明，RBE方法预测的RMS速度和时空能谱都显著依赖于参考平面的位置。压力边界条件的选取以及系统输入是否包含压力对于RBE的预测结果几乎没有影响。窗函数的选取不影响RBE预测的RMS速度，但是采用Hanning窗可以显著减少RBE预测的时空能谱的谱泄漏现象。增加参考平面的数目并不一定可以提升RBE方法的预测能力。

2.本文基于摩擦雷诺数170到1000的槽道湍流直接数值模拟数据研究了壁面上快变压力、慢变压力的自相关谱与互相关谱的特征，并且对于在构造壁面压力谱模型时快慢变压力互相关谱可以忽略的假设进行了数值验证。结果表明，在分贝刻度下，忽略快慢变压力互相关谱在流向波数、展向波数、频率一维谱上所造成的的最大误差分别为2dB、1dB和1dB。而对于二维谱和三维谱最大误差分别为2.4dB和5dB。对流特征线上的误差要显著小于位于对流特征线两侧的亚对流区和粘性区。

Space—time energy spectrum is a fundamental tool for the investigation of the dynamic coupling among turbulent motions at different space—time scales with broad engineering applications in turbulent generated noise and wind energy. In order to obtain the complete space—time energy spectra, the dataset of the flow field needs to cover all the length and time scales, ranging from Kolmogorov scales to the integral scales, in the problem of interest. This requirement is challenging for both numerical simulations and experimental measurements. Therefore, it is necessary to develop models which are consistent with the numerical and experimental data for the space—time spectra of velocity fluctuations and pressure fluctuations.

In this thesis, we numerically and theoretically study the space—time spectra of velocity fluctuations in the buffer layer and the space—time spectra of wall pressure. The main contributions of this thesis are summarized as follows:

1. The resolvent-based estimation method (RBE method) is applied to predict the root-mean-square (RMS) and space—time energy spectra of streamwise velocity fluctuation, where the input is the space—time energy spectra at a reference horizontal plane in the logarithmic layer and the output is the space—time energy spectra in the buffer layer. The explicit formulas for the RBE method are given in discrete form for numerical implementation. The results show the capability of the RBE method in the prediction of convection velocity and bandwidth of the space—time energy spectra. Furthermore, we make a systematic evaluation of the performance of the RBE method by varying the input configurations, including the wall-normal location of the reference plane, the inclusion or exclusion of the pressure as an input variable, the implementation approach of the pressure boundary conditions, the choice of the window functions and the number of reference planes. It is found that the results of both RMS velocity and space—time energy spectra obtained from the RBE method are sensitive to the location of the reference plane. However, the pressure boundary conditions and inclusion of pressure as an input do not cause significant change in the predicted RMS velocity and space—time energy spectra. Although it does not influence the prediction of the RMS velocity, a Hanning window is found crucial for the prediction of the space—time energy spectra. Simply increasing the number of reference planes will not improves the performance of the RBE method.

2. Based on the data from direct numerical simulations of channel flows with friction Reynolds number ranging from 170 to 1000, the characteristics of the space—time spectra and co-spectra of rapid wall pressure and slow wall pressure are investigated. Furthermore, the assumption that the co-spectra of rapid wall pressure and slow wall pressure are negligible in the development of models of the space—time spectra of wall pressure is verified numerically. It is found that the maximum errors in decibel scale caused by neglecting the rapid—slow pressure co-spectra in streamwise wavenumber, spanwise wavenumber and frequency spectra are 2dB, 1dB and 1dB, respectively. As for the two-dimensional spectra and three dimensional spectra, the maximum error is 2.4dB and 5dB, respectively. Compared with the sub-convective region and viscous region, the error along the convection characteristic line is very small.