Liutex (vortex) core and tube identification and automatic generation algorithms

As the third-generation (3 rd -G) of vortex identification (VI) methods, the physical quantities of Liutex were rigorously defined and systematically explored. These milestone researches in VI include the three forms of vortex descriptions based on the Liutex scalar, vector and tensor, which makes it possible to apply the Liutex core-line and tube to represent vortex structures. However, these intriguing structures are yet to be effectively generated and visualized. In the paper, the current status of vortex core-line generation is reviewed and thereby an effective discriminant method is obtained with the three important criteria, namely C-1, C-2 and C-3, which permits the core-line automatic identification algorithm being developed to uniquely generate vortex core-lines. With the core-line unique generation issue being resolved, the vortex tube is further explored and the vortex tube identification algorithm is developed. The vortex core-line and tube along with their generation algorithms are validated and presented by the DNS data for the natural transition in a zero-pressure gradient flat-plate (ZPGFP). The state-of-the-art vortex visualization technique demonstrates that the vortex core-line and tube can well represent and reflect the topological structures of vortex, which is distinctively distinguished themselves from the traditional VIs based on the iso-surface of the ad-hoc vortex discriminants, such as the well-known Q, Δ, λ 2, λ ci and lately the Ω criteria. The present researches significantly enrich the 3 rd -G VI system based on the Liutex theory and importantly provide a unique tool to explore the intrinsic natures of the centennial puzzle of turbulence and other vortex-related phenomena in future researches and engineering applications.