Abstract
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.
Highlights
A vortex is recognized as the rotational motion of fluids
Many researchers widely acknowledged the concept of vortex defined as the vorticity concentration and other vorticity-based methods [2, 3] as the vorticity vector was believed to offer a mathematical definition of fluid rotational motion
The results are presented in the following graph where the x-axis represents the relative stretching rate, and the y-axis gives the corresponding values of different vortex identification methods
Summary
A vortex is recognized as the rotational motion of fluids. Within the last several decades, a lot of vortex identification methods have been developed to track the vortical structure in a fluid flow; we still lack unambiguous and universally accepted vortex identification criteria. It is found that 1G and several 2G vortex identification methods misinterpret shearing and stretching as a constituent of vortical structure, which is not true These methods have dimensional problems at different physical levels, which are discussed in section 4 in detail.
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