Abstract
Modern views on the nature of the Kelvin–Helmholtz (KH) instability and its manifestations in the solar corona, in the interplanetary medium, and at the geomagnetospheric boundary are under consideration. We briefly describe the main theoretical results of the KH instability obtained in the linear approximation. Analysis of observational data, confirming the occurrence of the KH instability in magnetic formations of the solar coronal plasma and on the daytime magnetopause, was mainly performed in the approximation of incompressibility. We show that the Rayleigh–Taylor instability can significantly enhance the KH instability in the above regions due to interface accelerations or its curvature. Special attention is focused on the compressibility effect on the supersonic shear flow instability in the solar wind (SW) and at the geomagnetic tail boundary where this instability is usually considered to be ineffective. We have shown that the phase velocity of oblique perturbations is substantially less than the flow velocity, and values of the growth rate and frequency range are considerably higher than when only taking velocity-aligned disturbances into account. We emphasize that the magnetic field and plasma density inhomogeneity which weaken the KH instability of subsonic shear flows, in the case of a supersonic velocity difference weaken the stabilizing effect of the medium compressibility, and can significantly increase the instability. Effective generation of oblique disturbances by the supersonic KH instability explains the observations of magnetosonic waves and the formation of diffuse shear flows in the SW and on the distant magnetotail boundary, as well as the SW-magnetosphere energy and impulse transfer.
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References
Ajabshirizadeh, A., Ebadi, H., Vekalati, R.E., Molaverdikhani, K.: 2015, The possibility of Kelvin–Helmholtz instability in solar spicules. Astrophys. Space Sci. 357, 33. DOI .
Axford, W.I.: 1964, Viscous interaction between the solar wind and the Earth’s magnetosphere. Planet. Space Sci. 12, 45.
Bame, S., Anderson, R., Asbridge, J., Baker, D., Feldman, W., Gosling, J., Hones, E., McComas, D., Jr., Zwickl, R.: 1983, Plasma regimes in deep geomagnetic tail – ISEE 3. Geophys. Res. Lett. 10, 912.
Bettarini, L., Landi, S., Rappazzo, F., Velli, M., Opher, M.: 2006, Tearing and Kelvin–Helmholtz instabilities in the heliospheric plasma. Astron. Astrophys. 452, 321. DOI .
Blumen, W.: 1970, Shear layer of an inviscid compressible fluid. J. Fluid Mech. 46, 763.
Blumen, W., Drazin, P.G., Billings, D.F.: 1975, Shear layer instability of an inviscid compressible fluid, Part 2. J. Fluid Mech. 71, 305.
Burlaga, L.: 1979, Magnetic field, plasmas, and coronal holes: the inner solar system. Space Sci. Rev. 23, 201.
Chandra, K.: 1973, Hydromagnetic stability of plane heterogeneous shear flow. J. Phys. Soc. Japan 34, 539.
Chandrasekhar, S.: 1961, Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford. 652 p.
Chen, Y., Song, H.Q., Li, B., Xia, L.D., et al.: 2010, Streamer waves driven by coronal mass ejections. Astrophys. J. 714, 644. DOI .
Coleman, P.: 1968, Turbulence, viscosity and dissipation in solar-wind plasma. Astrophys. J. 153, 371.
Doschek, G.A., McKenzie, D.E., Warren, H.P.: 2014, Plasma dynamic above solar flare soft X-ray loop tops. Astrophys. J. 788, 26.
Drazin, P.G., Davey, A.: 1977, Shear layer instability of an inviscid compressible fluid. Part 3. J. Fluid Mech. 82, 255.
Dungey, J.B.: 1963, Structure of the exosphere and adventure in velocity space. In: De Witt, C., Hieblot, J., Lebeau, A. (eds.) The Geophysics: The Earth Environment, Gordon & Breach, New York, 403.
Einaudi, G., Boncinelli, P., Dahlburg, R., Russel, B., Karpen, J.: 1999, Formation of the slow solar wind in a coronal streamer. J. Geophys. Res. 104, 521.
Feng, L., Inhester, B., Gan, W.Q.: 2013, Kelvin–Helmholtz instability of a coronal streamer. Astrophys. J. 774, 141. DOI .
Fletcher, R., Cargill, P.J., Antiochos, S.K., Gudiksen, B.V.: 2015, Structures in the outer solar atmosphere. Space Sci. Rev. 188, 211. DOI . doi:10.1088/2041-8205/729/1/L8.
Foullon, C., Verwichte, E., Nakariakov, V.M., Nykyri, K., Farrugia, C.J.: 2011a, Magnetic Kelvin–Helmholtz instability at the Sun. Astrophys. J. 729, L8.
Foullon, C., Lavraud, B., Luhmann, J.G., Farrugia, C.J., et al.: 2011b, Plasmoid releases in the heliospheric current sheet and associated coronal hole boundary layer evolution. Astrophys. J. 737, 16. DOI .
Goldstein, M.I., Roberts, D.A., Matthaeus, W.H.: 1995, Magnetohydrodynamic turbulence in the solar wind. Annu. Rev. Astron. Astrophys. 33, 283.
Gomez, D., DeLuca, E.E., Mininni, P.D.: 2016, Simulations of the Kelvin–Helmholtz instability driven by coronal mass ejections in the turbulent corona. Astrophys. J. 818, 126.
Gratton, F.T., Farrugia, C.J., Cowley, S.W.H.: 1996, Is the magnetopause Rayleigh–Taylor unstable sometimes? J. Geophys. Res. 101(A3), 4929.
Guglielmi, A.V., Potapov, A.S., Klain, B.I.: 2010a, Rayleigh–Taylor–Kelvin–Helmholtz combined instability at the magnetopause. Geomagn. Aeron. 50(8), 958. Special Issue 2
Guglielmi, A.V., Potapov, A.S., Klain, B.I.: 2010b, Solar. Terr. Phys. 15, 24 (original Russian text).
Helmholtz, H.L.F.: 1868, On the discontinuous movements of fluids. Sitz.ber. Preuss. Akad. Wiss. Berl. Phil.-Hist. Kl. 23, 215.
Holzwarth, V., Schmitt, D., Schüssler, M.: 2007, Flow instabilities of magnetic flux tubes. II. Longitudinal flow. Astron. Astrophys. 469, 11. DOI .
Hundhausen, A.: 1972, Coronal Expansion and Solar Wind, Springer, Heidelberg, 238.
Joarder, P.S., Nakariakov, V.M., Roberts, B.: 1997, A manifestation of negative energy waves in the solar atmosphere. Solar Phys. 176, 285. DOI .
Johnson, J.R., Wing, S., Delamere, P.A.: 2014, Kelvin–Helmholtz instability in planetary magnetospheres. Space Sci. Rev. 184, 1. DOI .
Kelvin, Lord (Thomson W.T.): 1871, Hydrokinetic solutions and observations. Philos. Mag. 42, 362.
Korzhov, N.P., Mishin, V.V., Tomozov, V.M.: 1984, On the role of plasma parameters and the Kelvin–Helmholtz instability in a viscous interaction of solar wind streams. Planet. Space Sci. 32, 1169.
Korzhov, N.P., Mishin, V.V., Tomozov, V.M.: 1985, On the viscous interaction of solar wind streams. Soviet Astron. 62, 371.
Kovalenko, V.A., Korzhov, N.P.: 1976, Semi-empirical model of the solar wind. Soviet Astron. 53, 148.
Landau, L.D.: 1944, Stability of tangential discontinuities in compressible fluid. C. R. (Dokl.) Acad. Sci. URSS 44, 139.
Leonovich, A.S.: 2011, MHD-instability of the magnetotail: global modes. Planet. Space Sci. 59, 402. DOI .
Leonovich, A.S., Mishin, V.V.: 2005, Stability of magnetohydrodynamic shear flows with and without bounding walls. J. Plasma Phys. 71, Part 5, 645. DOI .
Lee, L.C., Olson, J.V.: 1980, Kelvin–Helmholtz instability in the variation of geomagnetic pulsation activity. Geophys. Res. Lett. 7, 777.
Lemen, J.R., Title, A.M., Akin, D.J., Boerner, P.F., Chou, C., Drake, J.F., Duncan, D.W., et al.: 2012, The Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO). Solar Phys. 275, 17. DOI .
Michalke, A.: 1964, On the inviscid instability of the hyperbolic-tangent velocity profile. J. Fluid Mech. 19, 543.
Mishin, V.V.: 1980, About possible effects of MHD instability of the Earth’s magnetosphere boundary. Issled. Geomagn., Aèron. Fiz. Solntsa. 50, 150 (in Russian).
Mishin, V.V.: 1981, On the MHD instability of the Earth’s magnetopause and its geophysical effects. Planet. Space Sci. 29, 359.
Mishin, V.V.: 1993, Accelerated motions of the magnetopause as a trigger of the Kelvin–Helmholtz instability. J. Geophys. Res. 98(A12), 21365.
Mishin, V.V.: 2003, On the predominance of oblique disturbances in the supersonic shear layer instability of the geomagnetic tail boundary. Nonlinear Process. Geophys. 10, 351.
Mishin, V.V.: 2005, Velocity boundary layers in the distant geotail and the Kelvin–Helmholtz instability. Planet. Space Sci. 53, 157. DOI .
Mishin, V.V., Morozov, A.G.: 1983, On the effect of oblique disturbances on Kelvin–Helmholtz instability in viscous interaction of solar wind streams. Planet. Space Sci. 31, 821.
Mishin, V.V., Matyukhin, Yu.G.: 1986, Kelvin–Helmholtz instability on the magnetopause as a possible source of wave energy in the Earth’s magnetosphere. Geomagn. Aeron. (Engl. Transl.) 26, 952.
Mishin, V.V., Parkhomov, V.A., Tabanakov, I.V., Hayashi, K.: 2001, About “inclusion” of flute instability at the magnetopause during passing of the interplanetary magnetic cloud on January, 10 and 11 1997. Geomagn. Aeron. 41, 165 (in Russian). DOI .
Miura, A.: 1987, Simulation of Kelvin–Helmholtz instability at the magnetopause boundary. J. Geophys. Res. 92, 3195.
Miura, A.: 1992, Kelvin–Helmholtz instability at the magnetospheric boundary: dependence on the magnetosheath sonic Mach number. J. Geophys. Res. 97(10), 655.
Morozov, A.G., Mishin, V.V.: 1981, Influence of the magnetospheric boundary layer structure on Kelvin–Helmholtz instability. Geomagn. Aeron. 21, 1044.
Möstl, U.V., Temmer, M., Veronig, A.M.: 2013, The Kelvin–Helmholtz instability at coronal mass ejection boundaries in the solar corona: observations and 2.5D MHD simulations. Astrophys. J. Lett. 766, L12. DOI .
Nakamura, T.K.M., Daughton, W., Karimabadi, H., Eriksson, S.: 2013, Three-dimensional dynamics of vortex induced reconnection and comparison with THEMIS observations. J. Geophys. Res. 118, 5742. DOI .
Ofman, L., Thompson, B.J.: 2011, SDO/AIA observation of Kelvin–Helmholtz instability in the solar corona. Astrophys. J. 734, L11. DOI .
Parker, E.N.: 1964, Dynamical properties of stellar coronae and stellar winds. Astrophys. J. 139, 690.
Roberts, D.A., Goldstein, M.L., Matthaeus, W.H.: 1992, Velocity shear generation of solar wind turbulence. J. Geophys. Res. 97(A11), 17115.
Rosenbauer, H., Schwenn, R., Marsch, E., Meyer, B., Miggenrieder, H., Montgomery, M.D., et al.: 1977, A survey of initial results of the Helios plasma experiment. J. Geophys. Res. 82, 561.
Ryutova, M., Berger, T., Frank, Z., Tarbell, T., Title, A.: 2010, Observation of plasma instabilities in quiescent prominences. Solar Phys. 267, 75. DOI .
Shen, C., Liu, Z.X.: 1999, The coupling mode between Kelvin–Helmholtz and resistive instabilities in compressible plasmas. Phys. Plasmas 6(9), 2883.
Shibata, K., Ishido, Y., Acton, L.W., Strong, K.T., et al.: 1992, Observations of X-ray jets with the YOHKOH soft X-ray telescope. Publ. Astron. Soc. Japan 44, L173.
Shimojo, M., Hashimoto, S., Shibata, K., Hirayama, T., et al.: 1996, Statistical study of solar X-ray jets observed with YOHKOH soft X-ray telescope. Publ. Astron. Soc. Japan 48, 123.
Sibeck, D.G., Slavin, J.A., Smith, E.J.: 1987, ISEE-3 magnetopause crossing: evidence for the Kelvin–Helmholtz instability. In: Lui, A.T.Y. (ed.) Magnetotail Physics, J. Hopkins Press, Baltimore, 73.
Syrovatsky, S.I.: 1954, Instability of tangential discontinuities in a compressible medium. Sov. Phys. JETP 27, 121.
Syrovatsky, S.I.: 1957, Magnetic hydrodynamics. Sov. Phys. Usp. 62, 247.
Vasheghani Farahani, S., Van Doorsselaere, T., Verwichte, E., Nakariakov, V.M.: 2009, Propagating transverse waves in soft X-ray coronal jets. Astron. Astrophys. 498, L29. DOI .
Wedemeyer-Böhm, S., Lagg, A., Nordlund, A.: 2009, Coupling from the photosphere to the chromosphere and the corona. Space Sci. Rev. 144, 317.
Zhelyazkov, I., Zaqarashvili, T.V.: 2012, Kelvin–Helmholtz instability of kink waves in photospheric twisted flux tubes. Astron. Astrophys. 547, A14. DOI .
Zhelyazkov, I., Chandra, R., Srivastava, A.K., Mishonov, T.: 2015, Kelvin–Helmholtz instability of magnetohydrodynamic waves propagating on solar surges. Astrophys. Space Sci. 356, 231. DOI .
Zaqarashvili, T.V., Zhelyazkov, I., Ofman, L.: 2015, Stability of rotating magnetized jets in the solar atmosphere. I. Kelvin–Helmholtz instability. Astrophys. J. 813, 123. DOI .
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This work was supported by the Russian Foundation for Basic Research, grants Nos. 14-05-91165 and 15-05-05561.
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Dedicated to the memory of Dr. N.P. Korzhov.
Waves in the Solar Corona: From Microphysics to Macrophysics
Guest Editors: Valery M. Nakariakov, David J. Pascoe, and Robert A. Sych
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Mishin, V.V., Tomozov, V.M. Kelvin–Helmholtz Instability in the Solar Atmosphere, Solar Wind and Geomagnetosphere. Sol Phys 291, 3165–3184 (2016). https://doi.org/10.1007/s11207-016-0891-4
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DOI: https://doi.org/10.1007/s11207-016-0891-4