The third-generation vortex identification method of Liutex (previously called Rortex) was introduced by the team led by Prof. Chaoqun Liu from University of Texas at Arlington to mathematically extract the rigid rotation part from the fluid motion, and thus to define and visualize vortices. Unlike the vorticity-based first generation and the scalar-valued second generation, Q, λ₂, Δ and λ_ci methods for example, the Liutex vector provides a unique, mathematical and systematic way to define vortices and visualize vortical structures from multiple perspectives without ambiguity. In this article, we summarize the recent developments of the Liutex framework and discuss the Liutex theoretical system including its existence, uniqueness, stability, Galilean invariance, locality and globality, decomposition in tensor and vector forms, Liutex similarity in turbulence, and multiple Liutex-based vortex visualization methods including Liutex lines, Liutex magnitude iso-surfaces, Liutex-Ω method, and Liutex core line method, etc.. Thereafter, the six core elements of vortex identification, including (1) absolute strength, (2) relative strength, (3) local rotational axis, (4) vortex rotation axes, (5) vortex core size, (6) vortex boundary, are used as touchstones against which the Liutex vortex identification system is examined. It is demonstrated with illustrative examples that the Liutex system is able to give complete and precise information of all six core elements in contrast to the failure and inaccuracy of the first and second-generation methods. The important concept that vorticity cannot represent vortex and the superiority of the Liutex system over previous methods are reiterated and stated in appropriate places throughout the paper. Finally, the article concludes with future perspectives, especially the application of the Liutex system in studying turbulence mechanisms encouraged by the discovery of Liutex similarity law. As a newly defined physical quantity, Liutex may open a door for quantified vortex and turbulence research including Liutex (vortex) dynamics and lead the community out of the shadow of turbulence research which traditionally relies on observations, graphics, assumptions, hypotheses, and other qualitative analyses. An optimistic projection is that the Liutex system could be critical to investigation of the vortex dynamics in applications from hydrodynamics, aerodynamics, oceanography, meteorology, etc. and to research of the generation, sustenance, modelling and controlling of turbulence.

中文翻译：

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Liutex理论体系和涡旋识别的六个核心要素

由得克萨斯大学阿灵顿分校的刘超群教授带领的团队介绍了Liutex的第三代涡流识别方法（以前称为Rortex），以数学方法从流体运动中提取刚性旋转部分，从而定义和可视化涡旋。不同于基于涡-第一代和标量值的第二代，Q，λ ₂，Δ和λ _CI例如，Liutex向量方法提供了一种独特的，数学的和系统的方式来定义旋涡并从多个角度可视化旋涡结构而没有歧义。在本文中，我们总结了Liutex框架的最新发展，并讨论了Liutex理论体系，包括其存在性，唯一性，稳定性，伽利略不变性，局部性和全局性，张量和矢量形式的分解，湍流中的Liutex相似性以及多个Liutex-基于涡旋的可视化方法，包括Liutex线，Liutex量等值面，Liutex- Ω方法，以及Liutex核心线方法等。此后，确定涡旋的六个核心要素包括：（1）绝对强度，（2）相对强度，（3）局部旋转轴，（4）涡旋旋转轴，（5 ）漩涡核心尺寸（6）漩涡边界被用作检验Liutex漩涡识别系统的试金石。通过举例说明，与第一代和第二代方法的失败和不准确性相比，Liutex系统能够提供所有六个核心要素的完整而精确的信息。在整个论文的适当位置，重申并陈述了涡度不能代表涡旋的重要概念，并且Liutex系统相对于先前方法的优越性。最后，本文以未来的观点作为结束，特别是Liutex系统在研究湍流机理方面的应用，这是由于发现了Liutex相似定律而引起的。作为一种新定义的物理量，Liutex可能为包括Liutex（涡旋）动力学在内的量化涡旋和湍流研究打开一扇门，并使社区摆脱传统上依赖于观测，图形，假设，假设和其他定性的湍流研究的阴影。分析。乐观的预测是，Liutex系统对于在流体力学，空气动力学，海洋学，气象学等应用中研究涡旋动力学以及对湍流的产生，维持，建模和控制的研究至关重要。作为一种新定义的物理量，Liutex可能为包括Liutex（涡旋）动力学在内的量化涡旋和湍流研究打开一扇门，并使社区摆脱传统上依赖于观测，图形，假设，假设和其他定性的湍流研究的阴影。分析。乐观的预测是，Liutex系统对于研究流体动力学，空气动力学，海洋学，气象学等应用中的涡旋动力学以及对湍流的产生，维持，建模和控制的研究至关重要。作为一种新定义的物理量，Liutex可能为包括Liutex（涡旋）动力学在内的量化涡旋和湍流研究打开一扇门，并使社区摆脱传统上依赖于观测，图形，假设，假设和其他定性的湍流研究的阴影。分析。乐观的预测是，Liutex系统对于研究流体动力学，空气动力学，海洋学，气象学等应用中的涡旋动力学以及对湍流的产生，维持，建模和控制的研究至关重要。和其他定性分析。乐观的预测是，Liutex系统对于研究流体动力学，空气动力学，海洋学，气象学等应用中的涡旋动力学以及对湍流的产生，维持，建模和控制的研究至关重要。和其他定性分析。乐观的预测是，Liutex系统对于研究流体动力学，空气动力学，海洋学，气象学等应用中的涡旋动力学以及对湍流的产生，维持，建模和控制的研究至关重要。