论文标题
重新审视圆喷射的两点相似性
Two-point similarity in the round jet revisited
论文作者
论文摘要
分析了远距离射流中的流向方向的两点相关张量的相似性，在此处分析了光谱理论的效用。可分离的两点相关系数已成为这样一个论点的基础：沿流向方向的能量优化基础函数是傅立叶模式（从平衡相似性理论的方法中）。从计算和分析的角度来看，这自然是非常可取的。然而，目前的工作表明，即使在对数拉伸坐标中，两点相关量乘以雅各布也不是不变的。该结果直接影响了相对于光谱空间中相关函数的基于傅立叶的动机，相对于磁场的正交分解（POD）。已经证明，使用早期工作的建议的坐标转换，无法实现内核的位移不变形式。这种无能与手头湍流与理想的均匀湍流情况之间的基本差异有关。
The similarity of the two-point correlation tensor along the streamwise direction in the axi-symmetric jet far-field is analyzed, herein its utility in spectral theory. A separable two-point correlation coefficient has been the basis for the argument that the energy-optimized basis functions along the streamwise direction are Fourier modes (from the approach of equilibrium similarity theory). This would naturally be highly desirable both from a computational and an analytical perspective. The present work, however, shows that the two-point correlation tensor multiplied by the Jacobian is not displacement invariant even in logarithmically stretched coordinates. This result directly impacts the motivation for a Fourier-based representation of the correlation function in spectral space in relation to the Proper Orthogonal Decomposition (POD) of the field. It is demonstrated that a displacement invariant form of the kernel is impossible to achieve using the suggested coordinate transformations from earlier works. This inability is shown to be related to the fundamental differences between the turbulent flow at hand and the ideal case of homogeneous turbulence.
