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特性。然而，发卡涡具有复杂构型且可能与其他涡旋相互缠绕，导致其提取困难。本文提出一种在剪切驱动湍流中提取并分离发卡涡以进行系统研究的框架。该方法首先基于特定涡判据（如$\lambda_2$）采用区域增长策略提取一般涡旋区域，随后通过自上而下的渐进式$\lambda_2$等值面提取方法分离这些涡旋，最终构建反映涡旋空间邻近性与合并关系的层次化树结构。在分离单个涡旋后，提取其形状与取向信息，并根据几何特征、取向特征及物理特性识别候选发卡涡。基于几何与物理属性开发交互式可视化系统，以支持发卡涡的探索、分类与分析。此外，本文还展示了所提系统在其他类型流动中一般涡旋分析研究中的扩展应用案例。