Lagrangian chaotic saddles and objective vortices in solar plasmas

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Lagrangian chaotic saddles and objective vortices in solar plasmas

Abraham C.-L. Chian, Suzana S. A. Silva, Erico L. Rempel, Luis R. Bellot Rubio, Milan Gošić, Kanya Kusano, and Sung-Hong Park

Phys. Rev. E 102, 060201(R) – Published 3 December 2020

Abstract

We report observational evidence of Lagrangian chaotic saddles in plasmas, given by the intersections of finite-time unstable and stable manifolds, using an $\approx 22 h$ sequence of spacecraft images of the horizontal velocity field of solar photosphere. A set of 29 persistent objective vortices with lifetimes varying from 28.5 to 298.3 min are detected by computing the Lagrangian averaged vorticity deviation. The unstable manifold of the Lagrangian chaotic saddles computed for $\approx 11 h$ exhibits twisted folding motions indicative of recurring vortices in a magnetic mixed-polarity region. We show that the persistent objective vortices are formed in the gap regions of Lagrangian chaotic saddles at supergranular junctions.

Received 11 September 2020
Accepted 18 October 2020

DOI:https://doi.org/10.1103/PhysRevE.102.060201

Physics Subject Headings (PhySH)

Chaos Turbulence Vortex flows

Coherent structures Solar plasma

Nonlinear Dynamics

Authors & Affiliations

Abraham C.-L. Chian ^1,2,3,*, Suzana S. A. Silva ⁴, Erico L. Rempel ^3,4, Luis R. Bellot Rubio ⁵, Milan Gošić ^6,7, Kanya Kusano ¹, and Sung-Hong Park ¹

¹Institute for Space-Earth Environmental Research (ISEE), Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan
²School of Mathematical Sciences, University of Adelaide, Adelaide, SA 5005, Australia
³National Institute for Space Research (INPE), P.O. Box 515, São José dos Campos, São Paulo 12227-010, Brazil
⁴Institute of Aeronautical Technology (ITA), São José dos Campos, São Paulo 12228-900, Brazil
⁵Instituto de Astrofísica de Andalucía (CSIC), Apartado de Correos 3004, E-18080 Granada, Spain
⁶Lockheed Martin Solar and Astrophysics Laboratory, Palo Alto, California 94304, USA
⁷Bay Area Environmental Research Institute, Moffett Field, California 94035, USA

^*abraham.chian@gmail.com

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Issue

Vol. 102, Iss. 6 — December 2020

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Images

Figure 1
Lagrangian chaotic saddles. (a) Finite-time unstable manifolds given by b-FTLE computed from 19:25:29 UT on 2010 November 2 to 08:31:15 UT on 2010 November 2. (b) Finite-time stable manifolds given by f-FTLE computed from 19:25:29 UT on 2010 November 2 to 06:19:42 UT on 2010 November 3. The black pluses mark the Lagrangian centers of supergranular cells. (c) Lagrangian chaotic saddles (red points) determined by the intersections of the thresholded finite-time unstable (green) and stable (blue) manifolds obtained from Figs. 1 and 1, respectively, with the threshold of b-FTLE (f-FTLE) given by $0.3 \times 10^{- 4} (0.25 \times 10^{- 4}$ ), respectively. The white/magenta box marks a mixed-polarity region of magnetic fields dominated by vortical flows.
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Figure 2
Objective vortices. (a) IVD computed at the initial time of vortex M1 at 17:23:57 UT on 2010 November 2, where the vortex center (boundary) is indicated by the magenta cross (line), respectively. (b) LAVD computed for the lifetime of vortex M1 from 17:23:57 UT to 22:22:32 UT on 2010 November 2, where the vortex center (boundary) is indicated by the magenta cross (line), respectively. (c) The boundary of 29 persistent objective vortices detected by LAVD from 08:31:15 UT on 2010 November 2 to 06:19:42 UT on 2010 November 3, superposed by the mean line-of-sight magnetic field for the same time interval consisted of 1 vortex with lifetime ( $T$ ) $\approx$ 5 h (magenta, M), 5 vortices with 3.5 h $> T >$ 1.6 h (blue, B), 9 vortices with 1.6 h $> T >$ 0.9 h (green, G), and 14 vortices with 0.9 h $> T >$ 0.47 h (red, R). The white box marks the same magnetic mixed-polarity region as Fig. 1 where a sequence of 7 recurrent persistent objective vortices are detected during the entire time interval.
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Figure 3
Lagrangian view of photospheric turbulence at disk center of the quiet Sun. (a) The vortex boundary (magenta line) of persistent objective vortices detected from 08:31:15 UT to 19:25:29 UT on 2010 November 2, superposed by the finite-time unstable manifolds of Fig. 1. (b) The vortex boundary of persistent objective vortices detected from 19:25:29 UT on 2010 November 2 to 06:19:42 UT on 2010 November 3, superposed by the finite-time stable manifolds of Fig. 1. The vortex center (magenta cross) of persistent objective vortices, Lagrangian chaotic saddles (red), and the background line-of-sight magnetic field averaged over the time interval of the respective unstable and stable manifolds, superposed by (c) the thresholded finite-time unstable manifolds (green) with a threshold of $0.3 \times 10^{- 4}$ and (d) the thresholded finite-time stable manifolds (blue) with a threshold of $0.25 \times 10^{- 4}$ . The white box marks the same magnetic mixed-polarity region as in Figs. 1 and 2.
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