Objective Lagrangian Vortex Detection in the Solar Photosphere

Abstract

Vortices in the solar photosphere can be linked to a wide range of events, such as small-scale solar eruptions, wave excitation, and heating of the upper part of the solar atmosphere. Despite their importance in solar physics, most of the current studies on photospheric vortices are based on methods that are not invariant under time-dependent translations and rotations of the reference frame and are Eulerian; i.e., they are based on single snapshots of a velocity field and, therefore, do not convey information on the true long-term motion of fluid particles on a time-varying field. Another issue with methods for vortex detection is that typically they provide false identifications in highly compressible flows. This Letter presents a novel criterion that effectively removes wrong detections based on the geometry of the streamlines of the displacement vector of fluid elements and can be readily applied to other astrophysical flows. The new criterion is applied to the Lagrangian-averaged vorticity deviation (LAVD), which is a recently developed frame invariant vortex detection method. The advantage of LAVD is that it delimits the vortices’ outer boundaries precisely by following up the trajectories of fluid elements in space and time. The proposed method is compared with two other techniques using horizontal velocity fields extracted from Hinode satellite data.

Supergranular turbulence in the quiet Sun: Lagrangian coherent structures

“…For a finite time duration [t 0 , t 0 + τ], a Lagrangian vortex is defined as an evolving material domain filled with a nested family of convex tubular level surfaces of LAVD t 0 +τ t 0 with outward-decreasing LAVD values. In contrast to the Eulerian methods that detect instantaneous swirl-like structures that do not convey long-term information of fluid motions, it was demonstrated that the LAVD method is capable of detecting persistent vortical flows (Haller et al 2016;Rempel et al 2017;Silva et al 2018). For 2D incompressible, shearless, non-magnetized fluids, the center of objective vortices are usually co-spatial with a local maximum of the LAVD field (Haller et al 2016).…”

“…This is not necessarily true for highly compressible magnetized fluids with strong shear regions such as photospheric flows, for which we must allow some deviation from convexity to ensure that all vortex cores are captured. Moreover, Silva et al (2018) showed that in order to avoid false vortex detection in flows with strong shear, such as supergranulations, it is necessary to apply a postprocessing filter to the set of vortices detected by LAVD. The d-criterion, based on the geometry of the streamlines of the displacement vector field of fluid elements, is adopted to find vortex cores.…”

“…The displacement vectors are computed by advecting the neighboring particles for a given time and subtracting their initial positions from their final positions. For details, see Silva et al (2018). A LAVD vortex is considered a true vortex boundary if it surrounds a vortex core detected by the d-criterion.…”

“…Rempel et al (2017) extended the technique for detecting objective velocity vortices developed by Haller et al (2016) to objective magnetic vortices. Silva et al (2018) applied the LAVD technique of Haller et al (2016) and the Hinode dataset of Requerey et al (2018) to detect objective velocity vortices in the quiet-Sun, and introduced a d-criterion to avoid false vortex detection.…”

Objective magnetic vortex detection

“…Since IACD is based on the curl of B, it will be large on regions with rotation of magnetic field lines as well as shear regions, a problem shared with the LAVD operator in velocity fields. For a discussion on problems related to kinematic vortex detection in strong shear regions of observational velocity fields using LAVD, as well as possible solutions to these problems, see Silva et al [26].…”