The utility of the wavenumber-frequency spectrum for description and interpretation of wall pressure fluctuations beneath turbulent boundary layers has been amply demonstrated over the past decades. This representation is widely used in modelling the flow-induced noise due to boundary layers developing on vehicle surfaces. A recurring issue concerns the underlying assumptions of stationary and homogeneous wall pressure fields. Even on a flat plate, the turbulent boundary layer thickening violates the homogeneous assumption. A numerical experiment of a spatially evolving turbulent boundary layer on a flat plate provides detailed wall-pressure data to assess the stationarity and homogeneity assumptions in the computation of wavenumber-frequency spectra. High-order statistics, stationarity tests developed for random time series and modern signal processing tools, such as the empirical mode decomposition, are applied. In particular, it is shown that the nonhomogeneity due to the space-varying nature of the turbulent sources does not change the characteristics of the wavenumber-frequency representation of the wall pressure field.

中文翻译：

---

湍流边界层壁压力波数-频率表示中的平稳性和均匀性假设

在过去的几十年中，已经充分证明了波数频谱在描述和解释湍流边界层下面的壁面压力波动中的作用。由于在车辆表面形成边界层，因此该表示法广泛用于对由流动引起的噪声进行建模。一个反复出现的问题涉及固定壁压力场和均匀壁压力场的基本假设。即使在平板上，湍流边界层的加厚也违反了均匀假设。平板上空间演化湍流边界层的数值实验提供了详细的壁压数据，以评估波数-频谱计算中的平稳性和均匀性假设。高阶统计 应用针对随机时间序列开发的平稳性测试和现代信号处理工具，例如经验模式分解。特别地，示出了由于湍流源的空间变化性质而引起的不均匀性不会改变壁压力场的波数-频率表示的特性。