We investigate spanwise-coherent structures in the turbulent flow around airfoils, motivated by their connection with trailing-edge noise. We analyse well-resolved large-eddy simulations (LES) of the flow around NACA 0012 and NACA 4412 airfoils, both at a Reynolds number of 400 000 based on the chord length. Spectral proper orthogonal decomposition performed on the data reveals that the most energetic coherent structures are hydrodynamic waves, extending over the turbulent boundary layers around the airfoils with significant amplitudes near the trailing edge. Resolvent analysis was used to model such structures, using the mean field as a base flow. We then focus on evaluating the dependence of such structures on the domain size, to ensure that they are not an artefact of periodic boundary conditions in small computational boxes. To this end, we performed incompressible LES of a zero-pressure-gradient turbulent boundary layer, for three different spanwise sizes, with the momentum-thickness Reynolds number matching those near the airfoils trailing edge. The same coherent hydrodynamic waves were observed for the three domains. Such waves are accurately modelled as the most amplified flow response from resolvent analysis. The signature of such wide structures is seen in non-premultiplied spanwise wavenumber spectra, which collapse for the three computational domains. These results suggest that the spanwise-elongated structures are not domain-size dependent for the studied simulations, indicating thus the presence of very wide structures in wall-bounded turbulent flows.

中文翻译：

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平板和翼型周围的展向相干流体动力波

我们研究了翼型周围湍流中的展向相干结构，其动机是它们与后缘噪声的联系。我们根据弦长分析了 NACA 0012 和 NACA 4412 翼型周围流动的高分辨率大涡模拟 (LES)，两者的雷诺数均为 400 000。对数据进行的光谱适当正交分解表明，最具能量的相干结构是流体动力波，在翼型周围的湍流边界层上延伸，在后缘附近具有显着的振幅。使用平均场作为基流，使用溶解分析来模拟这种结构。然后，我们专注于评估此类结构对域大小的依赖性，以确保它们不是小型计算框中周期性边界条件的伪影。为此，我们对三种不同的展向尺寸进行了零压力梯度湍流边界层的不可压缩 LES，动量厚度雷诺数与翼型后缘附近的值相匹配。对于三个域观察到相同的相干流体动力波。这种波被精确地建模为来自解析分析的最大放大流量响应。这种宽结构的特征可以在非预乘展向波数谱中看到，它在三个计算域中崩溃。这些结果表明，对于所研究的模拟，展向细长结构不依赖于域大小，因此表明壁边界湍流中存在非常宽的结构。动量厚度雷诺数与翼型后缘附近的那些相匹配。对于三个域观察到相同的相干流体动力波。这种波被精确地建模为来自解析分析的最大放大流量响应。这种宽结构的特征可以在非预乘展向波数谱中看到，它在三个计算域中崩溃。这些结果表明，对于所研究的模拟，展向细长结构不依赖于域大小，因此表明壁边界湍流中存在非常宽的结构。动量厚度雷诺数与翼型后缘附近的那些相匹配。对于三个域观察到相同的相干流体动力波。这种波被精确地建模为来自解析分析的最大放大流量响应。这种宽结构的特征可以在非预乘展向波数谱中看到，它在三个计算域中崩溃。这些结果表明，对于所研究的模拟，展向细长结构不依赖于域大小，因此表明壁边界湍流中存在非常宽的结构。这种波被精确地建模为来自解析分析的最大放大流量响应。这种宽结构的特征可以在非预乘展向波数谱中看到，它在三个计算域中崩溃。这些结果表明，对于所研究的模拟，展向细长结构不依赖于域大小，因此表明壁边界湍流中存在非常宽的结构。这种波被精确地建模为来自解析分析的最大放大流量响应。这种宽结构的特征可以在非预乘展向波数谱中看到，它在三个计算域中崩溃。这些结果表明，对于所研究的模拟，展向细长结构不依赖于域大小，因此表明壁边界湍流中存在非常宽的结构。