Hairpin vortices are one of the most important vortical structures in turbulent flows. Extracting and characterizing hairpin vortices provides useful insight into many behaviors in turbulent flows. However, hairpin vortices have complex configurations and might be entangled with other vortices, making their extraction difficult. In this work, we introduce a framework to extract and separate hairpin vortices in shear driven turbulent flows for their study. Our method first extracts general vortical regions with a region-growing strategy based on certain vortex criteria (e.g., $\lambda_2$) and then separates those vortices with the help of progressive extraction of ($\lambda_2$) iso-surfaces in a top-down fashion. This leads to a hierarchical tree representing the spatial proximity and merging relation of vortices. After separating individual vortices, their shape and orientation information is extracted. Candidate hairpin vortices are identified based on their shape and orientation information as well as their physical characteristics. An interactive visualization system is developed to aid the exploration, classification, and analysis of hairpin vortices based on their geometric and physical attributes. We also present additional use cases of the proposed system for the analysis and study of general vortices in other types of flows.

翻译：发卡涡是湍流中最重要的涡旋结构之一。提取并表征发卡涡有助于深入理解湍流中的多种行为。然而，发卡涡具有复杂构型，且可能与其他涡旋相互纠缠，导致其提取困难。本研究提出了一种针对剪切驱动湍流中发卡涡的提取与分离框架。该方法首先基于特定涡旋判据（如$\lambda_2$准则）采用区域生长策略提取一般涡旋区域，随后通过自上而下渐进提取$\lambda_2$等值面的方式分离这些涡旋。由此构建的层次化树状结构反映了涡旋间的空间邻近性与合并关系。在分离单个涡旋后，提取其形状与朝向信息，并根据这些几何物理特征识别候选发卡涡。基于涡旋的几何与物理属性，开发了交互式可视化系统以辅助发卡涡的探索、分类与分析。此外，本文还展示了该系统在其他类型流动中一般涡旋分析研究的应用案例。