Abstract
Incompressible vortex flow are observed in a large variety of astrophysical plasmas such as the convection zone and the atmosphere of stars, in astrophysical jets in stellar winds and in planetary magnetospheres. More specifically, magnetohydrodynamic (MHD) simulations have shown that two large scale interlaced Alfvénic vortices structure the magnetic tail of Uranus at solstice time. Assuming identical vortices, we compute the general linear structure of the flow near their centers within the frame of ideal MHD. We then use the analytic results to interpret and qualify the vortices observed in a 3D MHD simulation of a fast rotating Uranus-type planet.
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References
Andersen, A., Bohr, T., Stenum, B., et al.: Anatomy of a bathtub vortex. Phys. Rev. Lett. 91(10), 104502 (2003). https://doi.org/10.1103/PhysRevLett.91.104502. https://ui.adsabs.harvard.edu/abs/2003PhRvL..91j4502A
Appl, S., Lery, T., Baty, H.: Current-driven instabilities in astrophysical jets. Linear analysis. Astron. Astrophys. 355, 818–828 (2000). https://ui.adsabs.harvard.edu/abs/2000A&A...355..818A
Battaglia, A.F., Canivete Cuissa, J.R., Calvo, F., et al.: The Alfvénic nature of chromospheric swirls. Astron. Astrophys. 649, A121 (2021). https://doi.org/10.1051/0004-6361/202040110. https://ui.adsabs.harvard.edu/abs/2021A&A...649A.121B. arXiv:2103.07366 [astro-ph.SR].
Bernstein, I.B., Frieman, E.A., Kruskal, M.D., et al.: An energy principle for hydromagnetic stability problems. Proc. R. Soc. Lond. Ser. A 244(1236), 17–40 (1958). https://doi.org/10.1098/rspa.1958.0023. https://ui.adsabs.harvard.edu/abs/1958RSPSA.244...17B
Brito, D., Cardin, P., Nataf, H.C., et al.: Experimental study of a geostrophic vortex of gallium in a transverse magnetic field. Phys. Earth Planet. Inter. 91(1–3), 77–98 (1995). https://doi.org/10.1016/0031-9201(95)03051-w
Chan, J.C.L.: The physics of tropical cyclone motion. In: Annual Review of Fluid Mechanics, vol. 37, pp. 99–128. Annual Reviews, Palo Alto (2005). https://doi.org/10.1146/annurev.fluid.37.061903.175702
Fujita, T.T.: Tornadoes and downbursts in the context of generalized planetary scales. J. Atmos. Sci. 38(8), 1511–1534 (1981). https://doi.org/10.1175/1520-0469(1981)038<1511:TADITC>2.0.CO;2. https://ui.adsabs.harvard.edu/abs/1981JAtS...38.1511F
Griton, L., Pantellini, F., Meliani, Z.: Three-dimensional magnetohydrodynamic simulations of the solar wind interaction with a hyperfast-rotating Uranus. J. Geophys. Res. Space Phys. 123(7), 5394–5406 (2018). https://doi.org/10.1029/2018JA025331. https://ui.adsabs.harvard.edu/abs/2018JGRA..123.5394G
Hefferon, J.: Linear Algebra, 3rd edn. Orthogonal Publishing L3C (2017)
Helmholtz, H.: Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen. J. Reine Angew. Math. 55, 25–55 (1858). https://doi.org/10.1515/crll.1858.55.25. zenodo.org/record/1448878
Klimenko, A.Y.: Strong swirl approximation and intensive vortices in the atmosphere. J. Fluid Mech. 738, 268–298 (2014). https://doi.org/10.1017/jfm.2013.557. https://ui.adsabs.harvard.edu/abs/2014JFM...738..268K. arXiv:1401.5841 [physics.flu-dyn]
Kuniyoshi, H., Shoda, M., Iijima, H., et al.: Magnetic tornado properties: a substantial contribution to the solar coronal heating via efficient energy transfer. Astrophys. J. 949(1), 8 (2023). https://doi.org/10.3847/1538-4357/accbb8. https://ui.adsabs.harvard.edu/abs/2023ApJ...949....8K. arXiv:2304.03010 [astro-ph.SR]
McKinney, J.C., Blandford, R.D.: Stability of relativistic jets from rotating, accreting black holes via fully three-dimensional magnetohydrodynamic simulations. Mon. Not. R. Astron. Soc. 394(1), L126–L130 (2009). https://doi.org/10.1111/j.1745-3933.2009.00625.x. https://ui.adsabs.harvard.edu/abs/2009MNRAS.394L.126M. arXiv:0812.1060 [astro-ph]
Miesch Mark, S.: Large-scale dynamics of the convection zone and tachocline. Living Rev. Sol. Phys. 2, 1 (2005). http://www.livingreviews.org/lrsp-2005-1
Moll, R., Cameron, R.H., Schüssler, M.: Vortices in simulations of solar surface convection. Astron. Astrophys. 533, A126 (2011). https://doi.org/10.1051/0004-6361/201117441. https://ui.adsabs.harvard.edu/abs/2011A&A...533A.126M. arXiv:1108.0800 [astro-ph.SR]
Nakamura, M., Meier, D.L.: Poynting flux-dominated jets in decreasing-density atmospheres. I. The nonrelativistic current-driven kink instability and the formation of “wiggled” structures. Astrophys. J. 617(1), 123–154 (2004). https://doi.org/10.1086/425337. https://ui.adsabs.harvard.edu/abs/2004ApJ...617..123N. arXiv:astro-ph/0406405 [astro-ph]
Nakamura, M., Uchida, Y., Hirose, S.: Production of wiggled structure of agn radio jets in the sweeping magnetic twist mechanism. New Astron. 6(2), 61–78 (2001). https://doi.org/10.1016/S1384-1076(01)00041-0. https://ui.adsabs.harvard.edu/abs/2001NewA....6...61N
Pantellini, F.: A physical model for the magnetosphere of Uranus at solstice time. Astron. Astrophys. 643, A144 (2020). https://doi.org/10.1051/0004-6361/202039143. https://ui.adsabs.harvard.edu/abs/2020A&A...643A.144P. arXiv:2010.05806 [astro-ph.EP]
Requerey, I.S., Cobo, B.R., Gošić, M., et al.: Persistent magnetic vortex flow at a supergranular vertex. Astron. Astrophys. 610, A84 (2018). https://doi.org/10.1051/0004-6361/201731842. https://ui.adsabs.harvard.edu/abs/2018A&A...610A..84R. arXiv:1712.01510 [astro-ph.SR]
Schiff, L.I.: A question in general relativity. Proc. Natl. Acad. Sci. USA 25, 391–395 (1939). https://doi.org/10.1073/pnas.25.7.391. europepmc.org/articles/pmc1077928
Silva, S.S.A., Verth, G., Rempel, E.L., et al.: Solar vortex tubes. II. On the origin of magnetic vortices. Astrophys. J. 915(1), 24 (2021). https://doi.org/10.3847/1538-4357/abfec2
Tóth, G., KováCs, D., Hansen, K.C., et al.: Three-dimensional mhd simulations of the magnetosphere of Uranus. J. Geophys. Res. Space Phys. 109(A11), A11210 (2004). https://doi.org/10.1029/2004JA010406. https://ui.adsabs.harvard.edu/abs/2004JGRA..10911210T
Tziotziou, K., Scullion, E., Shelyag, S., et al.: Vortex motions in the solar atmosphere. Space Sci. Rev. 219(1), 1 (2023). https://doi.org/10.1007/s11214-022-00946-8. https://ui.adsabs.harvard.edu/abs/2023SSRv..219....1T
Wang, W., Liu, R., Wang, Y.: Tornado-like evolution of a kink-unstable solar prominence. Astrophys. J. 834(1), 38 (2017). https://doi.org/10.3847/1538-4357/834/1/38. https://ui.adsabs.harvard.edu/abs/2017ApJ...834...38W. arXiv:1611.04667 [astro-ph.SR]
Webster, D.L., Whitten, R.C.: Which electromagnetic equations apply in rotating coordinates? Astrophys. Space Sci. 24(2), 323–333 (1973). https://doi.org/10.1007/BF02637159. https://ui.adsabs.harvard.edu/abs/1973Ap&SS..24..323W
Wedemeyer, S., Steiner, O.: On the plasma flow inside magnetic tornadoes on the Sun. Publ. Astron. Soc. Jpn. 66, S10 (2014) https://doi.org/10.1093/pasj/psu086. https://ui.adsabs.harvard.edu/abs/2014PASJ...66S..10W. arXiv:1406.7270 [astro-ph.SR]
Wedemeyer-Böhm, S., Scullion, E., Steiner, O., et al.: Magnetic tornadoes as energy channels into the solar corona. Nature 486(7404), 505–508 (2012). https://doi.org/10.1038/nature11202. https://ui.adsabs.harvard.edu/abs/2012Natur.486..505W
Zaqarashvili, T.V., Vörös, Z., Zhelyazkov, I.: Kelvin-Helmholtz instability of twisted magnetic flux tubes in the solar wind. Astron. Astrophys. 561, A62 (2014). https://doi.org/10.1051/0004-6361/201322808. https://ui.adsabs.harvard.edu/abs/2014A&A...561A..62Z. arXiv:1311.4383 [astro-ph.SR]
Zaqarashvili, T.V., Zhelyazkov, I., Ofman, L.: Stability of rotating magnetized jets in the solar atmosphere. I. Kelvin-Helmholtz instability. Astrophys. J. 813(2), 123 (2015). https://doi.org/10.1088/0004-637X/813/2/123. https://ui.adsabs.harvard.edu/abs/2015ApJ...813..123Z. arXiv:1510.01108 [astro-ph.SR]
Zhang, B., Delamere, P.A., Yao, Z., et al.: How Jupiter’s unusual magnetospheric topology structures its aurora. Sci. Adv. 7(15), eabd1204 (2021). https://doi.org/10.1126/sciadv.abd1204. https://ui.adsabs.harvard.edu/abs/2021SciA....7.1204Z. arXiv:2006.14834 [physics.space-ph]
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This work has been financially supported by the PLAS@PAR project and by the National Institute of Sciences of the Universe (INSU). Thank you to the anonymous reviewer for valuable comments which helped to improve the paper and to ease the task of the reader.
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Appendix: Explicit form of the matrices of the differential equation system
Appendix: Explicit form of the matrices of the differential equation system
Recalling the correspondence between the components of the 6 dimensional vector \(\mathbf{X}\) and the components of the magnetic field vector \(\mathbf{B}\) and the velocity vector \(\mathbf{u}\)
the \(6\times 6\) matrices in the system of differential equations (16) take the form
and
As the inverse of \(M_{r}\) is required to compute the matrix \(\tilde{M}_{\xi}=M_{r}^{-1} M_{\xi}\) and the vector \(\tilde{A}_{\xi}=M_{r}^{-1} A_{\xi}\) which appear in the normal form of the system of differential equations (18), we also give its explicit form hereafter:
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Pantellini, F. On the linear structure of the interlaced Alfvén vortices in the tail of Uranus at solstice. Astrophys Space Sci 369, 63 (2024). https://doi.org/10.1007/s10509-024-04332-4
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DOI: https://doi.org/10.1007/s10509-024-04332-4