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Collective Vortex Dynamics: From Isolated Vortices to their Communities

Lauren McClure, Suzana Silva, Gary Verth, Istvan Ballai, Viktor Fedun

Abstract

Small-scale vortical motions in the upper solar atmosphere are abundant and occupy about 2.8% of the photosphere at any given time. Although considerable work has focused on the detection and analysis of individual solar vortices, the interconnected and multi-scale behaviour of these coherent structures remains largely unexplored. We present a methodology for studying this behaviour through vortex interactions, to improve our understanding of how small- and large-scale photospheric flows contribute to energy transfer into the upper solar atmosphere and to the driving of solar activity. We represent vortices as a network of interacting structures. We apply a community detection algorithm to derive an optimal reduced network composed of highly interconnected vortex groups. From the interaction patterns and group structure, we define three roles within each community: peripheral, connector and hub. We then track both vortex communities and their member vortices from the photosphere into the chromosphere and across their lifetimes. On average, vortices assigned to these roles persist to greater heights in the chromosphere and have longer lifetimes than unclassified vortices. This shows that community detection can identify vortices with greater dynamical influence on the upper solar atmosphere. We also find that 32% to 58.6% of vortex communities exhibit global periodic behaviour following a helical path. This collective vortical motion may indicate an enhanced mechanism for wave excitation. Solar vortical community detection, therefore, offers a new framework for studying solar vortices and a new perspective on the importance of collective vortex dynamics.

Collective Vortex Dynamics: From Isolated Vortices to their Communities

Abstract

Small-scale vortical motions in the upper solar atmosphere are abundant and occupy about 2.8% of the photosphere at any given time. Although considerable work has focused on the detection and analysis of individual solar vortices, the interconnected and multi-scale behaviour of these coherent structures remains largely unexplored. We present a methodology for studying this behaviour through vortex interactions, to improve our understanding of how small- and large-scale photospheric flows contribute to energy transfer into the upper solar atmosphere and to the driving of solar activity. We represent vortices as a network of interacting structures. We apply a community detection algorithm to derive an optimal reduced network composed of highly interconnected vortex groups. From the interaction patterns and group structure, we define three roles within each community: peripheral, connector and hub. We then track both vortex communities and their member vortices from the photosphere into the chromosphere and across their lifetimes. On average, vortices assigned to these roles persist to greater heights in the chromosphere and have longer lifetimes than unclassified vortices. This shows that community detection can identify vortices with greater dynamical influence on the upper solar atmosphere. We also find that 32% to 58.6% of vortex communities exhibit global periodic behaviour following a helical path. This collective vortical motion may indicate an enhanced mechanism for wave excitation. Solar vortical community detection, therefore, offers a new framework for studying solar vortices and a new perspective on the importance of collective vortex dynamics.
Paper Structure (14 sections, 12 equations, 4 figures, 1 table)

This paper contains 14 sections, 12 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Bifrost Simulation Data
  4. Vortex Interactions
  5. Results
  6. Lifetimes of Photospheric Vortices
  7. Photospheric-Chromospheric Vortex Tubes
  8. Global Trajectories of Vortex Communities
  9. Discussion and Conclusion
  10. Vortex Detection
  11. The Gamma Method
  12. The dual-part Gamma Method
  13. Normalisation as a Preprocessing Step
  14. Peripheral, Connector and Hub Definitions

Figures (4)

  • Figure 1: Vortex detection results over the full field of view at $t=0$ seconds. Black streamlines in the main panels show the total induced velocity field, computed from the contributions of all detected vortices, while panels a–g show streamlines in grey of the actual simulated velocity fields. Panels e and g highlight the hub and peripheral vortices at this time frame. The top panel shows the normalised induced velocity magnitude, and the bottom panel shows the angle (in radians) between the velocity field and induced velocity vectors.
  • Figure 2: Histograms of property distributions for vortex communities (panels a, b) and individual vortices (panels c, e). Panels a and b show community size and duration. Panel e shows vortex tube length, and panel c shows vortex lifetime. Panel d shows an example community structure, where the centroid colours and vortex border colour indicates community membership, with each centroid surrounded by its member vortices. Marker faces are coloured by $|\gamma_i|$ and border colour indicates community membership. Vortices are linked by lines coloured by the mean induced velocity magnitude between each pair. Boxes highlight the peripheral, connector and hub (blue, black and purple).
  • Figure 3: Examples of vortex detections over their vertical extent or lifetime. Figures a-f show individual vortex detections, where the boundaries throughout their height range or lifetime are coloured by the circulation at that height/time. For these panels, the detected centre is coloured by vortex role - blue for peripheral, black for connector and purple for hub. This colour scheme is also used in figures g and h to represent the classified vortices, in which grey is any vortex that does not fall into any of the three classes. Panels g and h show a subset of detected vortices at different heights or times.
  • Figure 4: Community centroid trajectories over time in a fixed horizontal plane. Panels b, c, f and g show four examples exhibiting helical motion, whilst panels d and e show examples of directed and kinked motion, respectively. Finally, panel a shows an unclassified centroid trajectory, exhibiting no clear motion pattern. Spheres denote centroid positions and are coloured by time.