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 Λ - vortex and the formation of the ring-like vortex is formed separately from the Λ - 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 Λ - 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.

在这项研究中，基于Liutex定义的涡旋核心线的新方法（也称为Liutex核心线）被用于支持以下假设：涡旋环不是Λ-涡旋的一部分以及环-的形成。就像漩涡是与Λ分开形成的-漩涡。还使用适当的正交分解（POD）来分析平板流动过渡的发夹环区域中发生的开尔文-弗尔姆霍兹（KH）不稳定性，以了解环形涡旋形成的机理。名为改进的Liutex-Omega方法的新涡流识别方法可有效地用于可视化和观察3-D涡流结构的形状。可以在POD模式1中找到流向涡旋结构特征作为平均流量。其他POD模式分别为stremwise和spanwise结构，并具有由KH不稳定性引起的波动运动。此外，结果表明，POD模式是成对的，并具有相同的特性，例如振幅，模式形状和时间演变。涡旋核和POD结果证实了Λ -涡流不是自变形为发夹涡流，但是发夹涡流由KH不稳定LAMBDA涡流边界层流动过渡发展发夹涡流期间形成。