Innovative and automated method for vortex identification^★,★★

I. Description of the SWIRL algorithm

¹ IRSOL Istituto Ricerche Solari “Aldo e Cele Daccò” Locarno, Università della Svizzera italiana (USI), Via Patocchi 57 – Prato Pernice, 6605 Locarno-Monti, Switzerland
e-mail: jose.canivete@irsol.usi.ch
² Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science (ICS), University of Zurich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
³ Leibniz-Institut für Sonnenphysik (KIS), Schöneckstrasse 6, 79104 Freiburg i.Br., Germany

Received: 8 April 2022
Accepted: 7 October 2022

Abstract

Context. As a universally accepted definition of a vortex has not yet been established, the community lacks an unambiguous and rigorous method for identifying vortices in fluid flows. Such a method would be useful for conducting robust statistical studies on vortices in highly dynamical and turbulent systems such as the solar atmosphere.

Aims. We aim to develop an innovative and robust automated methodology for the identification of vortices based on local and global characteristics of the flow, while avoiding the use of a threshold that could potentially prevent the detection of weak vortices in the process.

Methods. We present a new method that combines the rigor of mathematical criteria with the global perspective of morphological techniques. The core of the method consists of an estimation of the center of rotation for every point of the flow that presents some degree of curvature in its neighborhood. For this purpose, we employed the Rortex criterion and combined it with morphological considerations of the velocity field. We then identified coherent vortical structures based on clusters of estimated centers of rotation.

Results. We demonstrate that the Rortex is a more reliable criterion than the swirling strength and the vorticity for the extraction of physical information from vortical flows, because it measures the rigid-body rotational part of the flow alone and is not biased by the presence of pure or intrinsic shears. We show that the method performs well in the context of a simplistic test case composed of two Lamb-Oseen vortices. We combined the proposed method with a state-of-the-art clustering algorithm to build an automated vortex identification algorithm. The algorithm was applied to an artificial flow composed of multiple Lamb–Oseen vortices, with a random noisy background, and to the turbulent flow of a simulated magneto-hydrodynamical Orszag-Tang vortex test. The results demonstrate the reliability and accuracy of the method.

Conclusions. The present automated vortex identification method can be considered a new tool for the detection and study of vortices in dynamical and turbulent (magneto)hydrodynamical flows. By applying the implemented algorithm to numerical simulations and observational data, as well as comparing it to existing detection methods, we seek to successively improve the reliability of the detections and, ultimately, our knowledge on swirling motions in the solar, stellar, and planetary atmospheres.