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Lagrangian coherent structures in space plasmas

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Abstract

Space plasmas can be described as conducting flows in a turbulent state, where fluid motion is determined by a host of kinetic and magnetic coherent structures of different types. Identifying and following the evolution of those structures is crucial for a deep understanding, and possibly, the forecasting of plasma behaviour. Lagrangian coherent structures constitute a recently devised theory to describe material transport in fluids, with mathematical approaches carefully developed to detect the main transport barriers responsible for controlling fluid flows. In this work, we review the application of this theory to space plasmas using numerical simulations and satellite observations. In particular, the results show that Lagrangian coherent structures can be used to better understand complex plasma phenomena in the solar atmosphere.

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  1. http://pencil-code.nordita.org/ and http://pencil-code.googlecode.com.

References

  • Y. Aljohani, V. Fedun, I. Ballai, S.S.A. Silva, S. Shelyag, G. Verth, New approach for analyzing dynamical processes on the surface of photospheric vortex tubes. Astrophys. J. 928(1), 3 (2022). https://doi.org/10.3847/1538-4357/ac56db

    Article  ADS  Google Scholar 

  • K.T. Alligood, T.D. Sauer, J.A. Yorke, Chaos: An Introduction to Dynamical Systems (Springer, New York, 1996)

    MATH  Google Scholar 

  • A. Badza, T.W. Mattner, S. Balasuriya, How sensitive are Lagrangian coherent structures to uncertainties in data? Phys. D 444, 133580 (2023)

    MathSciNet  MATH  Google Scholar 

  • A.F. Battaglia, J.R. Canivete Cuissa, F. Calvo, A.A. Bossart, O. Steiner, The Alfvénic nature of chromospheric swirls. 649, A121 (2021). https://doi.org/10.1051/0004-6361/202040110

  • F.J. Beron-Vera, Y. Wang, M.J. Olascoaga, G.J. Goni, G. Haller, Objective detection of oceanic eddies and the agulhas leakage. J. Phys. Oceanogr. 43, 1426 (2013)

    ADS  Google Scholar 

  • E.G. Blackman, Overcoming the backreaction on turbulent motions in the presence of magnetic fields. Phys. Rev. Lett. 77, 2694 (1996)

    ADS  Google Scholar 

  • V. Bommier, E.L. Degl’Innocenti, M. Landolfi, G. Molodij, Unnofit inversion of spectro-polarimetric maps observed with themis. Astron. Astrophys. 464, 323 (2007)

    ADS  Google Scholar 

  • D. Borgogno, D. Grasso, F. Pegoraro, T.J. Schep, Barriers in the transition to global chaos in collisionless magnetic reconnection. I. ridges of the finite time Lyapunov exponent field. Phys. Plasmas 18, 102307 (2011)

    ADS  Google Scholar 

  • A. Brandenburg, The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence. Astrophys. J. 550, 824 (2001)

    ADS  Google Scholar 

  • A. Brandenburg, K. Subramanian, Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417, 1 (2005)

    ADS  MathSciNet  Google Scholar 

  • J.R. Canivete Cuissa, O. Steiner, Innovative and automated method for vortex identification. I. Description of the SWIRL algorithm. Astron. Astrophys. 668, A118 (2022). https://doi.org/10.1051/0004-6361/202243740

    Article  ADS  Google Scholar 

  • A.C.-L. Chian, E.L. Rempel, G. Aulanier, B. Schmieder, S.C. Shadden, B.T. Welsch, A.R. Yeates, Detection of coherent structures in photospheric turbulent flows. Astrophys. J. 786, 51 (2014)

    ADS  Google Scholar 

  • A.C.-L. Chian, S.S.A. Silva, E.L. Rempel, M. Gošić, L.R.B. Rubio, K. Kusano, R.A. Miranda, I.S. Requerey, Supergranular turbulence in the quiet sun: Lagrangian coherent structures. Mon. Not. R. Astron. Soc. 488, 3076 (2019)

    ADS  Google Scholar 

  • A.C.-L. Chian, S.S.A. Silva, E.L. Rempel, L.R.B. Rubio, M. Gošić, K. Kusano, S.-H. Park, Lagrangian chaotic saddles and objective vortices in solar plasmas. Phys. Rev. E 102, 060201(R) (2020)

    ADS  Google Scholar 

  • A.C.-L. Chian, E.L. Rempel, S.S.A. Silva, L.B. Rubio, M. Gošić, Intensification of magnetic field in merging magnetic flux tubes driven by supergranular vortical flows. Mon. Not. R. Astron. Soc. 518, 4930 (2023)

    ADS  Google Scholar 

  • R.C. Colaninno, A. Vourlidas, Analysis of the velocity field of cmes using optical flow methods. Astrophys. J. 652, 1747 (2006)

    ADS  Google Scholar 

  • P. Démoulin, Extending the concept of separatrices to qsls for magnetic reconnection. Adv. Space Res. 37, 1269 (2006)

    ADS  Google Scholar 

  • F. Enrile, G. Besio, A. Stocchino, Shear and shearless Lagrangian structures in compound channels. Adv. Water Resour. 113, 141 (2018)

    ADS  MATH  Google Scholar 

  • M.V. Falessi, F. Pegoraro, T.J. Schep, Lagrangian coherent structures and plasma transport processes. J. Plasma Phys. 81(5), 495810505 (2015)

    Google Scholar 

  • G. Falkovich, K. Gawedzki, M. Vergassola, Particles and fields in fluid turbulence. Rev. Mod. Phys. 73, 913 (2001)

    ADS  MathSciNet  MATH  Google Scholar 

  • M. Farazmand, G. Haller, Computing lagrangian coherent structures from their variational theory. Chaos 22(1) (2012)

  • M. Farazmand, D. Blazevski, G. Haller, Shearless transport barriers in unsteady two-dimensional flows and maps. Phys. D 278–279, 44 (2014)

    MathSciNet  MATH  Google Scholar 

  • G. Froyland, P. Koltai, Detecting the birth and death of finite-time coherent sets. Commun. Pure Appl. Math. (2023) (accepted)

  • I. Giagkiozis, V. Fedun, E. Scullion, D.B. Jess, G. Verth, Vortex flows in the solar atmosphere: automated identification and statistical analysis. Astrophys. J. 869(2), 169 (2018). https://doi.org/10.3847/1538-4357/aaf797

    Article  ADS  Google Scholar 

  • G.D. Giannatale, M.V. Falessi, D. Grasso, F. Pegoraro, T. Schep, M. Veranda, D. Bonfiglio, S. Cappello, Lagrangian coherent structures as a new frame to investigate the particle transport in highly chaotic magnetic systems. J. Phys. Conf. Ser. 1125, 012008 (2018)

    Google Scholar 

  • F. Giannattasio, M. Stangalini, F. Berrilli, D.D. Moro, L.B. Rubio, Diffusion of magnetic elements in a supergranular cell. Astrophys. J. 788, 137 (2014)

    ADS  Google Scholar 

  • L. Gizon, A.C. Birch, Local helioseismology. Living Rev. Sol. Phys. 2, 6 (2005)

    ADS  Google Scholar 

  • M. Gošić, L.R.B. Rubio, D.O. Suárez, Y. Katsukawa, J.C. del Toro Iniesta, The solar internetwork. I. Contribution to the network magnetic flux. Astrophys. J. 797, 49 (2014)

  • L. Graftieaux, M. Michard, N. Grosjean, Combining piv, pod and vortex identification algorithms for the study of unsteady turbulent swirling flows. Meas. Sci. Technol. 12(9), 1422 (2001)

    ADS  Google Scholar 

  • M.A. Green, C.W. Rowley, A.J. Smits, Using hyperbolic lagrangian coherent structures to investigate vortices in bioinspired fluid flows. Chaos 20, 017510 (2010)

    ADS  MathSciNet  Google Scholar 

  • T. Gunther, H. Theisel, The state of the art in vortex extraction. Comput. Graph. Forum 37, 149 (2018)

    Google Scholar 

  • A. Hadjighasem, M. Farazmand, D. Blazevski, G. Froyland, G. Haller, A critical comparison of lagrangian methods for coherent structure detection. Chaos 27, 053104 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  • G. Haller, Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Phys. D 149, 248 (2001)

    MathSciNet  MATH  Google Scholar 

  • G. Haller, A variational theory of hyperbolic lagrangian coherent structures. Phys. D 240, 574 (2011)

    MathSciNet  MATH  Google Scholar 

  • G. Haller, Lagrangian coherent structures. Annu. Rev. Fluid Mech. 47, 137 (2015)

    ADS  MathSciNet  Google Scholar 

  • G. Haller, Transport Barriers and Coherent Structures in Flow Data (Cambridge University Press, Cambridge, 2023)

    MATH  Google Scholar 

  • G. Haller, F.J. Beron-Vera, Geodesic theory of transport barriers in two-dimensional flows. Phys. D 241(20), 1680–1702 (2012)

    MATH  Google Scholar 

  • G. Haller, A.C. Poje, Eddy growth and mixing in mesoscale oceanographic flows. Nonlinear Process. Geophys. 4, 223 (1997)

    ADS  Google Scholar 

  • G. Haller, T. Sapsis, Lagrangian coherent structures and the smallest lyapunov exponent. Chaos 21, 023115 (2011)

    ADS  MathSciNet  MATH  Google Scholar 

  • G. Haller, G. Yuan, Lagrangian coherent structures and mixing in two-dimensional turbulence. Phys. D 147, 352 (2000)

    MathSciNet  MATH  Google Scholar 

  • G. Haller, A. Hadjighasem, M. Farazmand, F. Huhn, Defining coherent vortices objectively from the vorticity. J. Fluid Mech. 795, 136 (2016)

    ADS  MathSciNet  MATH  Google Scholar 

  • G. Haller, S. Katsanoulis, M. Holzner, B. Frohnapfel, D. Gatti, Objective barriers to the transport of dynamically active vector fields. J. Fluid Mech. 905, A17 (2020)

    ADS  MathSciNet  MATH  Google Scholar 

  • G.-H. Hsu, E. Ott, C. Grebogi, Strange saddles and the dimension of their invariant manifolds. Phys. Lett. A 127, 199 (1988)

    ADS  MathSciNet  Google Scholar 

  • J.C.R. Hunt, A. Wray, P. Moin, Eddies, stream, and convergence zones in turbulent flows. Center for Turbulence Research Report CTR-S88 (1988). http://ctr.stanford.edu/Summer/201306111537.pdf

  • K. Ide, D. Small, S. Wiggins, Distinguished hyperbolic trajectories in time-dependent fluid flows: analytical and computational approach for velocity fields defined as data sets. Nonlinear Process. Geophys. 9, 237 (2002)

    ADS  Google Scholar 

  • K. Ide, D. Small, S. Wiggins, Distinguished hyperbolic trajectories in time-dependent fluid flows: analytical and computational approach for velocity fields defined as data sets. Nonlinear Process. Geophys. 9(3/4), 237–263 (2002)

    ADS  Google Scholar 

  • R.T. Ishikawa, M. Nakata, Y.Y. Katsukawa, Y. Masada, T.L. Riethmuller, Multi-scale deep learning for estimating horizontal velocity fields on the solar surface. Astron. Astrophys. 658, A142 (2022)

    ADS  Google Scholar 

  • J. Jeong, F. Hussain, On the identification of a vortex. J. Fluid Mech. 285, 69 (1995)

    ADS  MathSciNet  MATH  Google Scholar 

  • Y. Kato, S. Wedemeyer, Vortex flows in the solar chromosphere. I. Automatic detection method. Astron. Astrophys. 601, A135 (2017). https://doi.org/10.1051/0004-6361/201630082

    Article  ADS  Google Scholar 

  • S. Katsanoulis, M. Farazmand, M. Serra, G. Haller, Vortex boundaries as barriers to diffusive vorticity transport in two-dimensional flows. Phys. Rev. Fluids 5, 024701 (2020)

    ADS  Google Scholar 

  • R.M. Kerr, A. Brandenburg, Evidence for a singularity in ideal magnetohydrodynamics: implications for fast reconnection. Phys. Rev. Lett. 83, 1155 (1999)

    ADS  Google Scholar 

  • P. Keys, A. Reid, M. Mathioudakis, S. Shelyag, V.M. de Jorge Henriques, R. Hewitt, D.D. Moro, S. Jafarzadeh, D. Jess, M. Stangalini, High-resolution spectropolarimetric observations of the temporal evolution of magnetic fields in photospheric bright points. Astron. Astrophys. 633, A60 (2020)

  • V.S. Lukin, Self-organization in magnetic flux ropes. Phys. Plasmas Control. Fusion 56, 060301 (2014)

    ADS  Google Scholar 

  • J.A.J. Madrid, A.M. Mancho, Distinguished trajectories in time dependent vector fields. Chaos 19, 013111 (2009)

    ADS  MathSciNet  Google Scholar 

  • A.M. Mancho, D. Small, S. Wiggins, A comparison of methods for interpolating chaotic flows from discrete velocity data. Comput. Fluids 35(4), 416–428 (2006)

    MATH  Google Scholar 

  • C. Mendoza, A.M. Mancho, Hidden geometry of ocean flows. Phys. Rev. Lett. 105, 038501 (2010)

    ADS  Google Scholar 

  • C. Mendoza, A.M. Mancho, The lagrangian description of aperiodic flows: a case study of the kuroshio current. Nonlinear Process. Geophys. 19(4), 449–472 (2012)

    ADS  Google Scholar 

  • C. Mendoza, A.M. Mancho, S. Wiggins, Lagrangian descriptors and the assessment of the predictive capacity of oceanic data sets. Nonlinear Process. Geophys. 21(3), 677–689 (2014)

    ADS  Google Scholar 

  • R.A. Miranda, E.L. Rempel, A.C.-L. Chian, Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional navier-stokes equations. Chaos 23, 033107 (2013)

    ADS  MathSciNet  MATH  Google Scholar 

  • R.A. Miranda, E.L. Rempel, A.C.-L. Chian, A.B. Schelin, Lagrangian coherent structures at the onset of hyperchaos in two-dimensional flows, in Handbook of Applications of Chaos Theory, pp. 511–529 (Chapman and Hall/CRC, 2017)

  • D.D. Moro, S. Giordano, F. Berrilli, 3d photospheric velocity field of a supergranular cell. Astron. Astrophys. 472, 599 (2007)

    ADS  Google Scholar 

  • K. Mulleners, M. Raffel, The onset of dynamic stall revisited. Exp. Fluids 52, 779 (2011)

    Google Scholar 

  • M.M. Neamtu-Halic, D. Krug, G. Haller, M. Holzner, Lagrangian coherent structures and entrainment near the turbulent/non-turbulent interface of a gravity current. J. Fluid Mech. 877, 824 (2019)

    ADS  MathSciNet  MATH  Google Scholar 

  • P.J. Nolan, M. Serra, S.D. Ross, Finite-time lyapunov exponents in the instantaneous limit and material transport. Nonlinear Dyn. 100, 3825 (2020)

    Google Scholar 

  • A. Nordlund, Solar convection. Sol. Phys. 100, 209 (1985)

    ADS  Google Scholar 

  • A. Okubo, Horizontal dispersion of floatable particles in the vicinity of velocity singularities such as convergences. Deep-Sea Res. 17, 445 (1970)

    ADS  Google Scholar 

  • S.A. Orszag, C.-M. Tang, Small-scale structure of two-dimensional magnetohydrodynamic turbulence. J. Fluid Mech. 90, 129 (1979)

    ADS  Google Scholar 

  • S.B.N.T. Ouellette, I.I. Rypina, Generalized lagrangian coherent structures. Phys. D 372, 31 (2018)

    MathSciNet  MATH  Google Scholar 

  • K. Padberg, T. Hauff, F. Jenko, O. Junge, Lagrangian structures and transport in turbulent magnetized plasmas. New J. Phys. 9, 400 (2007)

    ADS  Google Scholar 

  • T. Peacock, J. Dabiri, Introduction to focus issue: Lagrangian coherent structures. Chaos 20, 017501 (2010)

    ADS  Google Scholar 

  • F. Pegoraro, D. Bonfiglio, S. Cappello, G.D. Giannatale, M.V. Falessi, D. Grasso, M. Veranda, Coherent magnetic structures in self-organized plasmas. Plasma Phys. Control. Fusion 61, 044003 (2019)

    ADS  Google Scholar 

  • U. Ramirez, N. Wang, A.T. Chartier, S. Datta-Barua, Superdarn evidence for convection-driven lagrangian coherent structures in the polar ionosphere. J. Geophys. Res. Space Phys. 124, 3573 (2019)

    ADS  Google Scholar 

  • E.L. Rempel, A.C.-L. Chian, R.A. Miranda, Chaotic saddles at the onset of intermittent spatiotemporal chaos. Phys. Rev. E 76, 056217 (2007)

    ADS  Google Scholar 

  • E.L. Rempel, A.C.-L. Chian, A. Brandenburg, Lagrangian coherent structures in nonlinear dynamos. Astrophys. J. Lett. 735, L9 (2011)

    ADS  Google Scholar 

  • E.L. Rempel, A.C.-L. Chian, A. Brandenburg, Lagrangian chaos in an abc-forced nonlinear dynamo. Phys. Scr. 86, 018405 (2012)

    ADS  Google Scholar 

  • E.L. Rempel, A.C.-L. Chian, A. Brandenburg, P.M. Noz, S. Shadden, Coherent structures and the saturation of a nonlinear dynamo. J. Fluid Mech. 729, 309 (2013)

  • E.L. Rempel, A.C.-L. Chian, F.J. Beron-Vera, S. Szanyi, G. Haller, Objective vortex detection in an astrophysical dynamo. Mon. Not. R. Astron. Soc. 466, L108 (2017)

    ADS  Google Scholar 

  • E.L. Rempel, T.F.P. Gomes, S.S.A. Silva, A.C.-L. Chian, Objective magnetic vortex detection. Phys. Rev. E 99, 043206 (2019)

    ADS  Google Scholar 

  • E.L. Rempel, R. Chertovskih, K.R. Davletshina, S.S.A. Silva, B.T. Welsch, A.C.-L. Chian, Reconstruction of photospheric velocity fields from highly corrupted data. Astrophys. J. 933, 2 (2022)

    ADS  Google Scholar 

  • I.S. Requerey, B.R. Cobo, M. Gošić, L.R.B. Rubio, Persistent magnetic vortex flow at a supergranular vertex. Astron. Astrophys. 610, A84 (2018)

    Google Scholar 

  • T. Roudier, M. Rieutord, D. Brito, F. Rincon, J.M. Malherbe, N. Meunier, T. Berger, Z. Frank, Mesoscale dynamics on the sun’s surface from hinode observations. Astron. Astrophys. 495, 945 (2009)

    ADS  Google Scholar 

  • G. Rubino, D. Borgogno, M. Veranda, D. Bonfiglio, S. Cappello, D. Grasso, Detection of magnetic barriers in a chaotic domain: first application of finite time lyapunov exponent method to a magnetic confinement configuration. Plasma Phys. Control. Fusion 57, 085004 (2015)

    ADS  Google Scholar 

  • B. Schmieder, Solar jets: Sdo and iris observations in the perspective of new mhd simulations. Front. Astron. Space Sci. 9, 820183 (2022)

    Google Scholar 

  • M. Serra, G. Haller, Objective eulerian coherent structures. Chaos 26, 053110 (2016)

    ADS  MathSciNet  MATH  Google Scholar 

  • S.C. Shadden, F. Lekien, J.E. Marsden, Definition and properties of lagrangian coherent structures from finite-time lyapunov exponents in two-dimensional aperiodic flows. Phys. D 212, 271 (2005)

    MathSciNet  MATH  Google Scholar 

  • S. Shelyag, M.M.F.P. Keenan, Mechanisms for mhd poynting flux generation in simulations of solar photospheric magnetoconvection. Astrophys. J. Lett. 753, L22 (2012)

    ADS  Google Scholar 

  • S. Shelyag, P. Keys, Vorticity in the solar photosphere. Astron. Astrophys. 526, A5 (2011)

    Google Scholar 

  • K. Shibata, T. Magara, Solar flares: magnetohydrodynamic processes. Living Rev. Sol. Phys. 8, 6 (2011)

    ADS  Google Scholar 

  • S.S.A. Silva, E.L. Rempel, T.F.P. Gomes, I.S. Requerey, A.C.-L. Chian, Objective lagrangian vortex detection in the solar photosphere. Astrophys. J. Lett. 863, L2 (2018)

    ADS  Google Scholar 

  • S.S.A. Silva, V. Fedun, G. Verth, E.L. Rempel, S. Shelyag, Solar vortex tubes: vortex dynamics in the solar atmosphere. Astrophys. J. 898, 137 (2020)

    ADS  Google Scholar 

  • S.S.A. Silva, G. Verth, E.L. Rempel, S.S.LA.C.A. Schiavo, V. Fedun, Solar vortex tubes. II. On the origin of magnetic vortices. Astrophys. J. 915, 24 (2021)

  • S.S.A. Silva, M. Murabito, S.J.M. Stangliani, G. Verth, I. Ballai, F. V., The importance of horizontal poynting flux in the solar photosphere. Astrophys. J. 927, 146 (2022)

  • S.S.A. Silva, M. Lennard, G. Verth, I. Ballai, E.L. Rempel, J. Warnecke, H. Iijima, H. Hotta, S.-H. Park, A.C. Donea, K. Kusano, V. Fedun, Novel approach to forecasting photospheric emergence of active regions. Astrophys. J. Lett. 948, L24 (2023)

    ADS  Google Scholar 

  • G.W. Simon, A.M. Title, K.P. Topka, T.D. Tarbell, R.A. Shine, S.H. Ferguson, H.Z. et al. Definition and properties of lagrangian coherent structures from finite-time lyapunov exponents in two-dimensional aperiodic flows. Astrophys. J. 327, 964 (1988)

  • S.H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Westview Press, Boulder, 2015)

    MATH  Google Scholar 

  • D.O. Suárez, Y. Katsukawa, L.R.B. Rubio, The connection between internetwork magnetic elements and supergranular flows. Astrophys. J. Lett. 758, L38 (2012)

    ADS  Google Scholar 

  • S. Tian, Y. Gao, X. Dong, C. Liu, Definitions of vortex vector and vortex. J. Fluid Mech. 849, 312 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  • C. Truesdell, W. Noll, The Nonlinear Field Theories of Mechanics (Springer, Berlin, 2004)

    MATH  Google Scholar 

  • K. Tziotziou, E. Scullion, S. Shelyag, O. Steiner, E. Khomenko, G. Tsiropoula, J.R.C. Cuissa, S. Wedemeyer, I. Kontogiannis, N. Yadav, I.N. Kitiashvili, S.J. Skirvin, I. Dakanalis, A.G. Kosovichev, V. Fedun, Vortex motion in the solar atmosphere. Space Sci. Rev. 219, 1 (2023)

    ADS  Google Scholar 

  • A.A. van Ballegooijen, D.H. Mackay, Model for the coupled evolution of subsurface and coronal magnetic fields in solar active regions. Astrophys. J. 659, 1713 (2007)

    ADS  Google Scholar 

  • A. Vögler, S. Shelyag, M. Schüssler, F. Cattaneo, T. Emonet, T. Linde, Simulations of magneto-convection in the solar photosphere. Astron. Astrophys. 429, 335 (2005)

  • J. Weiss, The dynamics of enstrophy transfer in two-dimensional hydrodynamics. Phys. D 48, 273 (1991)

    MathSciNet  MATH  Google Scholar 

  • B.T. Welsch, G.H. Fisher, W.P. Abbett, S. Regnier, Simulations of magneto-convection in the solar photosphere. Astrophys. J. 610, 1148 (2004)

    ADS  Google Scholar 

  • S. Wiggins, The dynamical systems approach to lagrangian transport in oceanic flows. Annu. Revi. Fluid Mech. 37, 295 (2005)

    ADS  MathSciNet  MATH  Google Scholar 

  • M.F. Woodard, Solar subsurface flow inferred directly from frequency-wavenumber correlations in the seismic velocity field. Astrophys. J. 565, 634 (2002)

    ADS  Google Scholar 

  • C.-C. Wu, T. Chang, Further study of the dynamics of two-dimensional mhd coherent structures—a large-scale simulation. J. Atmos. Sol. Terr. Phys. 63, 1447 (2001)

    ADS  Google Scholar 

  • W. Xu, Y. Gao, Y. Deng, J. Liu, C. Liu, An explicit expression for the calculation of the rortex vector. Phys. Fluids 31, 095102 (2019)

    ADS  Google Scholar 

  • A.R. Yeates, G. Hornig, B.T. Welsch, Lagrangian coherent structures in photospheric flows and their implications for coronal magnetic structures. Astron. Astrophys. 539, A1 (2012)

    ADS  Google Scholar 

  • X. Yu, L. Xu, Y. Yan, Image desaturation for sdo/aia using deep learning. Sol. Phys. 296, 56 (2021)

    ADS  Google Scholar 

  • Y. Yuan, S.S.A. Silva, V. Fedun, I.N. Kitiashvili, G. Verth, Advanced \(\gamma \) method for small-scale vortex detection in the solar atmosphere. Astrophys. J. Suppl. Ser. (2023)

  • J. Zhong, T.S. Huang, R.J. Adrian, Extracting 3d vortices in turbulent fluid flow. IEEE Trans. Pattern Anal. Mach. Intell. 20, 193 (1998)

    Google Scholar 

  • J. Zhou, R. Adrian, S. Balachandar, T. Kendall, Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353 (1999)

    ADS  MathSciNet  MATH  Google Scholar 

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Acknowledgements

E.L.R. acknowledges Brazilian agency CNPq (Grant 306920/2020-4). VF, GV, E.L.R. and SSAS are grateful to The Royal Society, International Exchanges Scheme, collaboration with Brazil (IES/R1/191114). VF, GV and SSAS are grateful to Science and Technology Facilities Council (STFC) grant ST/V000977/1. VF and GV thank The Royal Society, International Exchanges Scheme, collaboration with Chile (IE170301), Greece (IES/R1/221095), India (IES/R1/211123), Spain (IES/R2/212183) and Australia (IES/R3/213012). MG was supported by NASA contract NNM07AA01C (Solar-B (Hinode) Focal Plane Package Phase E). This research has also received financial support from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 824135 (SOLARNET). RAM acknowledges Brazilian agency CNPq (Grants 407493/2022-0 and 407341/2022-6).

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Rempel, E.L., Chian, A.CL., de S. A. Silva, S. et al. Lagrangian coherent structures in space plasmas. Rev. Mod. Plasma Phys. 7, 32 (2023). https://doi.org/10.1007/s41614-023-00136-1

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