Topological Separation of Vortices

TL;DR

This paper introduces a topological vortex separation method that improves the accuracy of vortex segmentation in turbulent flows by extending contour tree techniques with a layering process and statistical correction.

Contribution

It presents a novel vortex separation approach combining contour tree segmentation with layering and statistical correction to better distinguish individual vortices.

Findings

Significant improvement in vortex separation accuracy.

Reduction of incorrect splits in vortex regions.

Enhanced quantification of vortex statistics.

Abstract

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.