Hairpin vortices are fundamental structures within turbulent boundary layers, playing a crucial role in energy dissipation, mixing, and momentum transport. However, accurately extracting these structures remains challenging due to their irregular shapes, varying scales, and entanglement with surrounding vortical structures. This article presents a novel framework for the extraction of hairpin vortices from turbulent boundary layers. The method begins by identifying vortical regions and decomposing them into smaller segments using merge tree-based segmentation. A novel bottom-up rejoining approach is then introduced to group candidate segments according to the geometric and physical characteristics of hairpin vortices, resulting in regions that encompass complete hairpin vortex structures. These regions are subsequently refined and validated through skeleton analysis to detect the characteristic hairpin shape and are further confirmed using additional scalar-based criteria. Finally, smooth enclosing surfaces are generated for effective visualization. To enable quantitative evaluation, reference hairpin vortices are extracted from several flow datasets and used as ground truth. Compared with existing approaches, the proposed method eliminates manual parameter tuning, reduces under- and over-segmentation, and significantly improves both accuracy and computational efficiency. Demonstrations on multiple turbulent flow cases show that the method is robust and effective for hairpin vortex extraction under varying boundary layer conditions.

Vortices and their analysis play a critical role in the understanding of complex phenomena in turbulent flows. Traditional vortex extraction methods, notably region-based techniques, often overlook the entanglement phenomenon, resulting in the inclusion of multiple vortices within a single extracted region. Their separation is necessary for quantifying different types of vortices and their statistics. In this study, we propose a novel vortex separation method that extends the conventional contour tree-based segmentation approach with an additional step termed "layering". Upon extracting a vortical region using specified vortex criteria (e.g., λ2), we initially establish topological segmentation based on the contour tree, followed by the layering process to allocate appropriate segmentation IDs to unsegmented cells, thus separating individual vortices within the region. However, these regions may still suffer from inaccurate splits, which we address statistically by leveraging the continuity of vorticity lines across the split boundaries. Our findings demonstrate a significant improvement in both the separation of vortices and the mitigation of inaccurate splits compared to prior methods.