LAUSR

As a milestone research in vortex identification (VI), the physical quantity of Liutex, including its forms of scalar, vector and tensor, was systematically explored and rigorously obtained as the third-generation (3G) of the vortex definition and identification methods distinguished from the first generation (1G) by vorticity and the second generation (2G) by the vortex identification (VI) criteria solely dependent on the velocity gradient tensor eigenvalues. Based on these findings, the vortex-core lines were abstracted from the well-defined Liutex, and for the first time, were automatically generated and massively visualized using computer. The distinctive characteristics of these vortex cores with the intriguing threshold-independency make them be the uniquely appropriate entity to represent and to depict the vortex structures in turbulence. The letter made use of the DNS data for the natural transition in a zero-pressure gradient flat-plate (Type-A turbulent boundary layer (TBL)) and the fully-developed turbulence in a square annular duct (Type-B TBL) to demonstrate the vortex structure represented by the vortex-core lines. The 3G VI approach based on the vortex-core lines is capable of profoundly uncovering the vortex natures. Moreover, the capability of automatically identifying the vortex cores and massively visualizing the large number of vortex-core behaviors in a transient way will enable the fluid-mechanics and other related-science communities to step into a new era to explore the intrinsic natures of the centennial puzzle of turbulence and other vortex-related phenomena in future.