涡旋的拓扑分离
Topological Separation of Vortices
AI总结：
本研究提出一种基于等高线树与分层步骤的涡旋分离方法，利用涡量线连续性统计修正分割，显著提升涡旋分离准确率。
摘要：
涡旋及其分析在理解湍流复杂现象中起着关键作用。传统的涡旋提取方法，尤其是基于区域的技术，常常忽视纠缠现象，导致单个提取区域内包含多个涡旋。为了量化不同类型的涡旋及其统计特性，必须对它们进行分离。在本研究中，我们提出了一种新颖的涡旋分离方法，该方法在传统的基于等高线树的分割方法基础上，增加了一个称为“分层”的额外步骤。在使用指定的涡旋判据（如 $\lambda_2$）提取涡旋区域后，我们首先基于等高线树建立拓扑分割，随后通过分层过程为未分割的单元分配适当的分割标识，从而将区域内的各个涡旋分离开来。然而，这些区域仍可能遭受不准确的分割，我们通过利用涡量线在分割边界上的连续性进行统计处理来解决这一问题。我们的研究结果表明，与先前方法相比，在涡旋分离和减少不准确分割方面均有显著改进。
英文摘要：
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., $λ_2$), 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.
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