  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.
