Liutex core line and POD analysis on hairpin vortex formation in natural flow transition

In this study, the new method of the vortex core line based on Liutex definition, also known as Liutex core line, is applied to support the hypothesis that the vortex ring is not a part of the ? - vortex and the formation of the ring-like vortex is formed separately from the ? - vortex. The proper orthogonal decomposition (POD) is also applied to analyze the Kelvin-VHelmholtz (K-H) instability happening in hairpin ring areas of the flow transition on the flat plate to understand the mechanism of the ring-like vortex formation. The new vortex identification method named modified Liutex-Omega method is efficiently used to visualize and observe the shapes of vortex structures in 3-D. The streamwise vortex structure characteristics can be found in POD mode one as the mean flow. The other POD modes are in stremwise and spanwise structures and have the fluctuation motions, which are induced by K-H instability. Moreover, the result shows that POD modes are in pairs and share the same characteristics such as amplitudes, mode shapes, and time evolutions. The vortex core and POD results confirm that the ? - vortex is not self-deformed to a hairpin vortex, but the hairpin vortex is formed by the K-H instability during the development of Lambda vortex to hairpin vortex in the boundary layer flow transition.