Chaoqun Liu - Liutex and Third Generation of Vortex Definition and Identification: An Invited Workshop from Chaos 2020

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This book is a collection of papers presented in the invited workshop, Liutex and Third Generation of Vortex Definition and Identification for Turbulence, of CHAOS2020 conference, Florence, Italy, June 913, 2020. Due to the COVID-19 pandemic, the meeting was finally held online as a virtual conference. We had 33 registered speakers and 30 papers are published in this book including one invited paper.

Liutex is a new physical quantity discovered by Prof. Chaoqun Liu at the University of Texas at Arlington (UTA) in 2018 (Liu et al., Physics of Fluids 30, 2018) to represent fluid rotation or vortex. The discovery of Liutex is probably one of the most important breakthroughs in modern fluid kinematics especially for vortex science and turbulence research. Vortex is ubiquitous in nature and viewed as the building blocks, the muscles, and sinews of turbulent flows (Kchemann, J. Fluid Mech., 21, 1965). However, vortex had no mathematical definition before the discovery of Liutex, which was the bottleneck of modern fluid dynamics and caused countless confusion in vortex and turbulence research. Kol (V. Kol and J. stek, Phys. Fluids 32, 091702, 2020) pointed out that Rortex is a mathematically rigorous tool suitable for vortex characterization. Xu (Liutex and Its Applications in Turbulence Research, ISBN-13: 978-0128190234, ISBN-10: 012819023X, Elsevier, 2020) made comments that Liutex does lift and uncover the mask covering vortex which has puzzled our science community for so many centuries. Specifically, the Liutex core-lines limpidly bring out the skeleton of vortex structures and for the first time, vividly exhibit these structures to our visual world, which, from Xus experience, is so far the unique representation of vortical structures with the true, only true, nothing else but the true mathematical essences of vortex physics in entirety.

Since vortex is the building block of turbulence, without mathematical definition of vortex, turbulence research is in general limited to qualitative study which is in general relied on observation, graphics, movies, approximations, assumptions, guesses, and hypotheses. The rigorous mathematical definition of vortex or Liutex will bring turbulence research to a new era from qualitative study to quantified research.

According to Liu et al. (Journal of Hydrodynamics, 31(2):119, 2019), there are three generations of vortex identification methods in history. In 1858, Helmholtz first defined vortex as a vortex tube composed of the so-called vortex filaments, which are really infinitesimal vorticity tubes. It is classified as the first generation of vortex identification that vortex is defined as vorticity tubes. Science and engineering applications have shown that the correlation between vortex and vorticity is very weak, especially in the near-wall region. During the past four decades, many vortex identification criteria, Q, , 2 and ci methods (Hunt et al. 1988; Chong et al. 1990; Jeong et al. 1995; Zhou et al. 1999; Chakraborty 2005) for example, have been developed, which are classified as the second generation of vortex identification. They are all based on the eigenvalues of the velocity gradient tensor. However, they are all scalars and thus strongly dependent on the factitious and arbitrary threshold, when plotting the iso-surface to represent the vortical structures. In addition, they all lack physical meanings and obviously are contaminated by stretching (compression) and shearing. Liutex as the third generation of vortex definition and identification was developed by Liu and his students at UTA (Liu et al., Physics of Fluids 30:035103, 2018; Gao et al., Physics of Fluids, 30:085107, 2018). Liutex is defined as a vector which uses the real eigenvector of velocity gradient tensor as its direction and twice the local angular speed of the rigid rotation as its magnitude. The major idea of Liutex is to extract the rigid rotation part from fluid motion to represent vortex. After almost two hundred years of efforts, for the first time, Liutex, an accurate physical quantity to represent fluid rotation or vortex, was born in UTA.

After that, a number of vortex identification methods have been developed by Liu and his UTA Team including Liutex vector, Liutex vector lines, Liutex tubes, Liutex iso-surface, Liutex-Omega methods, Objective Liutex, and, more recently, Liutex Core Line and Tube methods which can more accurately visualize the vortical structures in turbulent flows, demonstrated by countless users in research papers. Liutex Core Line, which is defined as a special Liutex line, where the gradient of R is parallel to Liutex vector, is unique and threshold-free.

A so-called Principal Coordinate based on the velocity gradient tensor is defined and the fundamental vector and tensor decompositions are made in the Principal Coordinate by Liu and his students. A new vorticity decomposition to Liutex and shear, namely RS decomposition of vorticity, is proposed by Liu to separate non-dissipative rigid rotation from dissipative shear by decomposition of vorticity (Liu et al., Physics of Fluids 30:035103, 2018). A new Liutex-based