Abstract
The Liutex-core line method is a milestone product in the 3G VI, which makes the Liutex be distinguished from the 1st and 2nd generations of VI using the traditional vortex visualization based on iso-surface approach. The method limpidly takes out the skeleton of vortex structures and for the first time, offers an opportunity to uniquely represent and vividly exhibit these vortical structures to our visual world. Based on the core-line definition in the Liutex theory, the chapter explains the Liutex-core lines manual generation procedures. Moreover, for the first time, presents the automatic generation approach using computer which opens the door to massively visualize the vortex structures in turbulence. The characteristics of Liutex-core lines and their advantages over the traditional iso-surface presentation are profoundly elucidated in terms of the core-line threshold-independency and their unique appropriateness to depict the vortex structures in turbulence.Another important and beauty part in the Liutex theory is the R-S decomposition which clearly explains our current misunderstandings of vortex based on the vorticity and practically provide a capability to study the Liutex dynamics. The current chapter makes use of the recent DNS data to demonstrate a detailed roadmap to combine the Helmholtz equation and the R-S decomposition to rigorously investigate the dynamics of vortices in the transition leading to turbulence. The Liutex-core line enables and confirms a number of in-depth findings, such as the Mode A and B secondary instabilities as well as the hairpin pattern in the transition of cylinders in tandem.
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