In large eddy simulations (LESs), the large scales of turbulent motion are resolved directly, whereas the small scales that are computationally expensive to solve are modeled. The scale separation is performed either in the physical domain (space or time) or in Fourier space, which involves application of an explicit or implicit scale filtering operation, parting the resolved and subfilter-scales (well known as subgrid scales). Proper orthogonal decomposition (POD) of a turbulent flow also leads to the scale separation, where the POD modes represent characteristic scales of motion. In the present work, the similarity between the physical and Fourier scales and the POD modes, in terms of their kinetic-energy content and the interchange of energy among the scales and modes, is used to model the effect of subfilter-scales of motion for the LES. The subfilter-scales stress tensors, namely, Leonard, cross, and Reynolds are expressed directly in terms of the POD modes, while the cross and Reynolds subfilter-scale stresses are modeled, incorporating the energy contribution of the subfilter-scale POD modes. In addition to the mathematical properties of the subfilter-scale stress tensor, the model inherently predicts the near-wall asymptotic behavior and the backward transfer of subfilter-scale energy (the backscatter).

中文翻译：

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大涡模拟的正交正交分解辅助子尺度尺度湍流模型

在大型涡流模拟（LESs）中，直接解决了大尺度的湍流运动，而对解决了计算上昂贵的小尺度进行了建模。在物理域（空间或时间）或傅立叶空间中执行标度分离，这涉及应用显式或隐式标度过滤操作，将解析的和子过滤器标度（众所周知的子网格标度）分开。湍流的正确正交分解（POD）也导致尺度分离，其中POD模式代表运动的特征尺度。在目前的工作中，物理和傅立叶标度与POD模式之间的相似性，就它们的动能含量以及这些标度和模式之间的能量交换而言，可用于模拟运动的子过滤器标度的影响。 LES。子过滤器尺度的应力张量，即伦纳德，克罗斯和雷诺兹，直接以POD模式表示，而交叉和雷诺兹子过滤器尺度应力则是模型化的，并结合了子过滤器尺度POD模式的能量贡献。除了子滤波器级应力张量的数学特性外，该模型还固有地预测了近壁渐近行为和子滤波器级能量的向后传递（反向散射）。