用于Liutex/Rortex和其他涡流识别方法的拉伸和剪切污染分析
Stretching and Shearing Contamination Analysis for Liutex/Rortex and Other Vortex Identification Methods
摘要：
虽然传统的涡识别方法如Q、Delta、Lambda 2、Lambdaci等在涡的识别和可视化方面仍然很流行，但这些方法将剪切和拉伸作为涡强度的一部分。然而，剪切和拉伸并不有助于流体旋转。本文研究了拉伸和剪切的污染效应，并与Liutex法进行了比较。从我们的调查，流体是一个准确的定义流体旋转或涡，而其他涡识别方法受到不同程度的拉伸和剪切的污染。为了唯一性，速度梯度张量的分解只能在所谓的主坐标中进行。本文推导了Liutex与其它涡识别函数之间的数学关系，研究了剪切和拉伸对不同涡识别方法的影响。不同格式下拉伸和剪切效应的数学公式和计算结果表明，Liutex方法只考虑流体的局部刚性旋转，而其它方法只考虑拉伸/压缩和剪切作为流体旋转或旋涡的一部分，因此Liutex方法比其它旋涡识别方法具有优越性。
英文摘要：
Although traditional vortex identification methods such as Q, Delta, Lambda2, Lambdaci remain popular in the identification and visualization of vortices, these methods count on shearing and stretching as a part of vortex strength. However, shearing and stretching do not contribute to fluid rotation. In this paper, the contamination effects of stretching and shearing of these methods are investigated and compared with Liutex method. From our investigation, the Liutex is an exact definition of fluid rotation or vortex, while other vortex identification methods are contaminated by stretching and shearing at different levels. The decomposition of the velocity gradient tensor can only be conducted in a so-called Principal Coordinate for uniqueness. The mathematical relation between Liutex and other vortex identification function are derived in this paper and then the effects of shearing and stretching on different vortex identification methods are studied. The mathematical formula and computation of the stretching and shearing effects on different schemes clearly show that the Liutex method has superiority over the other vortex identification methods as it only counts on local fluid rigid rotation while other methods count on stretching/compression and shearing as a part of the fluid rotation or vortex.
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