Solar Vortex Detection With Velocity Field Normalisation: Eliminating False Positives

TL;DR

The paper tackles the challenge of reliably detecting small-scale solar photospheric vortices, where shear artefacts in non-uniform flows cause false positives. It proposes a simple preprocessing step that normalises the velocity field to unit magnitude and tests four established vortex-detection criteria—IVD, $λ_2$, $Q$, and the Γ method—on high-resolution Bifrost simulations, using the $d$-criterion as a pseudo ground truth for rotation. The results show that unit-vector normalisation significantly reduces false detections for $Q$, $λ_2$, and IVD, improves boundary definition, and yields more consistent detections across methods, while the Γ method, though accurate, under-detects vortices. The study demonstrates a practical, physics-based enhancement that can be readily adopted to improve vortex identification in solar and other turbulent flows, with potential implications for accurately quantifying the contribution of vortical motions to energy transport.

Abstract

Small-scale vortices in the solar photosphere play a central role in transporting mass, energy, and momentum into the upper solar atmosphere, yet reliably detecting these structures remains rather challenging. We address this problem by introducing a simple preprocessing step that normalises the velocity field by its magnitude. Our method preserves flow topology while suppressing shear-induced artefacts that lead to spurious detections in non-uniform, high-rotation environments. For validation, we apply this approach to high-resolution Bifrost simulations and evaluate vortex detection using four commonly employed methods: IVD, the $λ_2$-criterion, the Q-criterion, and the $Γ$ method. We assess which structures exhibit physically consistent rotation by using the $d$-criterion to automatically detect rotational plasma-flow features, which we use as an approximate ground truth. We find that, in the unnormalised field, a substantial fraction of detections made by the first three methods are false positive detections. Normalisation removes most of these. The $Γ$ method detects true vortices but misses a large number of vortical flows. The normalisation step yields better-defined and more realistic vortex boundaries. As the $Γ$ method underpins most observational analyses, current studies likely capture only a subset of vortical flows. By comparison, the other three methods detect four to five times more vortices after normalisation, suggesting that the true photospheric vortex coverage may be underestimated by a similar factor. Overall, this physically motivated preprocessing step enhances the accuracy and physical realism of vortex detection and offers a practical enhancement for analysing vortical flows in turbulent flows.

Figures (10)

• Figure 1: A view of the vertical component of velocity, $v_z$, over the numerical domain over which we conduct our analyses. The blue and black box represent the subdomain shown in Appendix ( the blue blox is shown in Figure (\ref{['fig:6']}) and the black box represents the subdomain shown in Figures (\ref{['fig:7']}--\ref{['fig:10']})).
• Figure 2: Detection results for a structure across all four techniques. The boundary associated with the AVF detection is displayed in red, and the UVF detected boundary in green. If no such boundary is shown, the method did not flag a vortex in this location. The horizontal unnormalised velocity field is shown in quiver plots and streamlines for each method.
• Figure 3: The number of reported detections per each time frame for the: AVF detections (orange solid line), validated AVF detections (orange dashed line), UVF detections (blue solid line) and the validated UVF detections (blue dashed line).
• Figure 4: Normalised histograms for the convexity deficiency (Eq. \ref{['NS']}) of UVF and AVF detections validated by a $d$-criterion centre. UVF is shown in blue, while AVF in orange.
• Figure 5: Normalised histograms for the area of UVF and AVF detections that have been validated. As before, UVF is shown in blue, AVF in orange.