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., $\lambda_2$), 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.

翻译：涡旋及其分析在理解湍流中的复杂现象方面起着关键作用。传统的涡旋提取方法，特别是基于区域的技术，常常忽略纠缠现象，导致在单个提取区域内包含多个涡旋。对这些涡旋进行分离对于量化不同类型的涡旋及其统计特性是必要的。在本研究中，我们提出了一种新颖的涡旋分离方法，该方法扩展了传统的基于轮廓树的分割方法，增加了一个称为"分层"的步骤。在使用指定的涡旋准则（例如 $\lambda_2$）提取涡旋区域后，我们首先基于轮廓树建立拓扑分割，随后通过分层过程为未分割的单元分配适当的分割ID，从而分离区域内的各个涡旋。然而，这些区域可能仍然存在不准确的分割，我们通过利用跨越分割边界的涡量线的连续性，从统计上解决了这个问题。我们的研究结果表明，与先前的方法相比，该方法在涡旋分离和减少不准确分割方面均有显著改进。