The newly developed vortex-identification method, Liutex, has provided a new systematic description of the local fluid rotation, which includes scalar, vector, and tensor forms. However, the advantages of Liutex over the other widely used vortex-identification methods such as Q, ∆, λ2, and λci have not been realized. These traditional methods count on shearing and stretching as a part of vortex strength. But, in the real flow, shearing and stretching do not contribute to fluid rotation. In this paper, the decomposition of the velocity gradient tensor is conducted in the Principal Coordinate for uniqueness. Then the contamination effects of stretching and shearing of the traditional methods are investigated and compared with the Liutex method in terms of mathematical analysis and numerical calculations. The results show that the Liutex method is the only method that is not affected by either stretching or shear, as it represents only the local fluid rigid rotation. These results provide supporting evidence that Liutex is the superior method over others.

中文翻译：

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Liutex拉伸和剪切污染分析以及其他涡旋识别方法

新开发的涡旋识别方法Liutex为局部流体旋转提供了新的系统描述，其中包括标量，矢量和张量形式。但是，与其他广泛使用的涡流识别方法（例如Q，Δ，λ2和λci）相比，Liutex的优势尚未实现。这些传统方法依靠剪切和拉伸作为涡旋强度的一部分。但是，在实际流动中，剪切和拉伸不会导致流体旋转。在本文中，速度梯度张量的分解是在主坐标系中进行的，以实现唯一性。然后研究了传统方法的拉伸和剪切的污染效应，并在数学分析和数值计算方面将其与Liutex方法进行了比较。结果表明，Liutex方法是唯一不受拉伸或剪切影响的方法，因为它仅表示局部流体的刚性旋转。这些结果提供了支持性证据，表明Liutex是优于其他方法的方法。