EAGER: Development and Application of Liutex and Third Generation of Vortex Definition and Identification

旋涡被直观地认为是流体的旋转/漩涡运动。涡旋在宇宙中无处不在，影响着人类的生活和环境。人类面临着生存和灾难性的威胁，在许多情况下，这些威胁主要是由涡旋造成的，例如人类引起的气候变化导致极端天气、前所未有的飓风和危及生命的龙卷风。此外，大流行和污染引起的呼吸系统和心脏疾病十分猖獗。在许多这样的灾难性事件中，涡旋起到了关键作用。此外，漩涡控制湍流和噪波生成的动力学。然而，涡旋没有严格的定义，现有的涡旋识别方法不准确、不合适，所展示的湍流涡旋结构也不是唯一的。该项目的目标是开发一个全面的Liutex和第三代涡旋的定义和识别。对局部流体旋转和全局旋涡的严格数学定义将进一步修改，使之具有唯一性、准确性和适用于旋涡科学和湍流研究的特点。将开发一个高阶涡旋识别软件--LiutexUTA、改进的Liutex-OmegaUTA、Liutex-Core-LineUTA方法，并分发给湍流研究界。揭示了发夹涡形成的关键问题--三维流涡的形成机理。将开发新的基于Liutex的流体运动学，以指导教育和研究中的流体动力学。将研究新的Liutex/Vortex动力学，并将重新讨论新的流体动力学控制方程，并将根据研究进展提出新的想法。该奖项反映了NSF的法定使命，并已通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Vortex is intuitively recognized as a rotational/swirling motion of fluids. Vortex is omnipresent in the universe and affects human life and the environment. Humanity is faced with existential and catastrophic threats which are largely caused by vortex in many cases, such as human-induced climate change leads to extreme weather, unprecedented hurricanes, and life-threatening tornados. In addition, pandemic and pollution-induced respiratory and heart diseases are rampant. In many of these catastrophic events, the vortex plays a key role. In addition, vortex controls the dynamics of turbulence and noise generation. However, vortex had no rigorous definition, existing vortex identification methods are not accurate and appropriate, and the demonstrated vortex structure of turbulence is not unique. The goal of this project is to develop a comprehensive Liutex and third generation of vortex definition and identification. The rigorous mathematical definition of local fluid rotation and global vortex will be further modified to be unique, accurate and appliable to vortex science and turbulence research. A high-order vortex identification software – LiutexUTA, Modified Liutex-OmegaUTA, Liutex-Core-LineUTA methods – will be developed and distributed to the turbulence research community. The 3-D Liutex generation mechanism will be revealed, which is a key issue of the hairpin vortex formation. The new Liutex-based Fluid Kinematics will be developed to guide fluid dynamics in education and research. The new Liutex/Vortex dynamics will be investigated, and the new fluid dynamics governing equations will be revisited and new ideas will be presented based on the research progress.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.