The sources of wall-pressure fluctuations in turbulent channel flow are studied using a novel framework. The wall-pressure power spectral density (PSD) $(\unicode[STIX]{x1D719}_{pp}(\unicode[STIX]{x1D714}))$ is expressed as an integrated contribution from all wall-parallel plane pairs, $\unicode[STIX]{x1D719}_{pp}(\unicode[STIX]{x1D714})=\int _{-\unicode[STIX]{x1D6FF}}^{+\unicode[STIX]{x1D6FF}}\int _{-\unicode[STIX]{x1D6FF}}^{+\unicode[STIX]{x1D6FF}}\unicode[STIX]{x1D6E4}(r,s,\unicode[STIX]{x1D714})\,\text{d}r\,\text{d}s$ , using the Green’s function. Here, $\unicode[STIX]{x1D6E4}(r,s,\unicode[STIX]{x1D714})$ is termed the net source cross-spectral density (CSD) between two wall-parallel planes, $y=r$ and $y=s$ and $\unicode[STIX]{x1D6FF}$ is the half-channel height. Direct numerical simulation data at friction Reynolds numbers of 180 and 400 are used to compute $\unicode[STIX]{x1D6E4}(r,s,\unicode[STIX]{x1D714})$ . Analysis of the net source CSD, $\unicode[STIX]{x1D6E4}(r,s,\unicode[STIX]{x1D714})$ reveals that the location of dominant sources responsible for the premultiplied peak in the power spectra at $\unicode[STIX]{x1D714}^{+}\approx 0.35$ (Hu et al., AIAA J., vol. 44, 2006, pp. 1541–1549) and the wavenumber spectra at $\unicode[STIX]{x1D706}^{+}\approx 200$ (Panton et al., Phys. Rev. Fluids, vol. 2, 2017, 094604) are in the buffer layer at $y^{+}\approx 16.5$ and 18.4 for $Re_{\unicode[STIX]{x1D70F}}=180$ and 400, respectively. The contribution from a wall-parallel plane (located at distance $y^{+}$ from the wall) to wall-pressure PSD is log-normal in $y^{+}$ for $\unicode[STIX]{x1D714}^{+}>0.35$ . A dominant inner-overlap region interaction of the sources is observed at low frequencies. Further, the decorrelated features of the wall-pressure fluctuation sources are analysed using spectral proper orthogonal decomposition (POD). Instead of the commonly used $L^{2}$ inner product, we require the modes to be orthogonal in an inner product with a symmetric positive definite kernel. Spectral POD supports the case that the net source is composed of two components – active and inactive. The dominant spectral POD mode that comprises the active part contributes to the entire wall-pressure PSD. The suboptimal spectral POD modes that constitute the inactive portion do not contribute to the PSD. Further, the active and inactive parts of the net source are decorrelated because they stem from different modes. The structure represented by the dominant POD mode at the premultiplied wall-pressure PSD peak inclines in the downstream direction. At the low-frequency linear PSD peak, the dominant mode resembles a large scale vertical pattern. Such patterns have been observed previously in the instantaneous contours of rapid pressure fluctuations by Abe et al. (2005, Fourth International Symposium on Turbulence and Shear Flow Phenomena, Begel House Inc.).

中文翻译：

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湍流通道直接数值模拟分析壁面压力波动源

使用新框架研究湍流通道流中壁压波动的来源。壁压功率谱密度 (PSD) $(\unicode[STIX]{x1D719}_{pp}(\unicode[STIX]{x1D714}))$ 表示为所有壁平行平面对的积分贡献， $\unicode[STIX]{x1D719}_{pp}(\unicode[STIX]{x1D714})=\int _{-\unicode[STIX]{x1D6FF}}^{+\unicode[STIX]{x1D6FF}} \int _{-\unicode[STIX]{x1D6FF}}^{+\unicode[STIX]{x1D6FF}}\unicode[STIX]{x1D6E4}(r,s,\unicode[STIX]{x1D714})\, \text{d}r\,\text{d}s$ ，使用格林函数。这里，$\unicode[STIX]{x1D6E4}(r,s,\unicode[STIX]{x1D714})$ 被称为两个壁平行平面之间的净源交叉谱密度（CSD），$y=r$ $y=s$ 和 $\unicode[STIX]{x1D6FF}$ 是半通道高度。摩擦雷诺数为 180 和 400 的直接数值模拟数据用于计算 $\unicode[STIX]{x1D6E4}(r,s,\unicode[STIX]{x1D714})$ 。对净源 CSD 的分析，$\unicode[STIX]{x1D6E4}(r,s,\unicode[STIX]{x1D714})$ 表明主要源的位置负责功率谱中的预乘峰值在 $\ unicode[STIX]{x1D714}^{+}\approx 0.35$ (Hu et al., AIAA J., vol. 44, 2006, pp. 1541–1549) 和 $\unicode[STIX]{x1D706 处的波数谱}^{+}\approx 200$ (Panton et al., Phys. Rev. Fluids, vol. 2, 2017, 094604) 在 $y^{+}\approx 16.5$ 和 $Re_ 18.4 的缓冲层中{\unicode[STIX]{x1D70F}}=180$ 和 400，分别。对于 $\unicode[STIX]{x1D714}，壁平行平面（位于距离壁 $y^{+}$）对壁压力 PSD 的贡献是 $y^{+}$ 中的对数正态分布^{+}>0.35$。在低频下观察到源的主要内部重叠区域相互作用。此外，使用频谱适当的正交分解（POD）分析壁压力波动源的去相关特征。代替常用的 $L^{2}$ 内积，我们要求模式在具有对称正定核的内积中是正交的。Spectral POD 支持净源由两个组件组成的情况 - 活动和非活动。包括活动部分的主要光谱 POD 模式对整个壁压力 PSD 有贡献。构成非活动部分的次优光谱 POD 模式对 PSD 没有贡献。此外，网络源的活动和非活动部分是去相关的，因为它们源自不同的模式。预乘壁压PSD峰的主要POD模式所代表的结构向下游方向倾斜。在低频线性 PSD 峰值处，主导模式类似于大尺度垂直模式。这种模式之前已经在 Abe 等人的快速压力波动的瞬时轮廓中观察到。（2005 年，第四届湍流和剪切流现象国际研讨会，Begel House Inc.）。