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In situ multi-satellite detection of coherent vortices as a manifestation of Alfvénic turbulence

An Erratum to this article was published on 08 September 2005


Turbulence in fluids1 and plasmas2,3,4,5 is a ubiquitous phenomenon driven by a variety of sources—currents, sheared flows, gradients in density and temperature, and so on. Turbulence involves fluctuations of physical properties on many different scales, which interact nonlinearly to produce self-organized structures in the form of vortices2,3,4,5. Vortex motion in fluids and magnetized plasmas is typically governed by nonlinear equations2,3,4,5, examples of which include the Navier–Stokes equation1,2, the Charney–Hasegawa–Mima equations2,3,4,5 and their numerous generalizations6,7,8,9. These nonlinear equations admit solutions2,3,4,5 in the form of different types of vortices that are frequently observed in a variety of contexts: in atmospheres, in oceans and planetary systems2,4, in the heliosphere10,11, in the Earth's ionosphere and magnetosphere12,13,14,15,16,17, and in laboratory plasma experiments18. Here we report the discovery by the Cluster satellites19 of a distinct class of vortex motion—short-scale drift-kinetic Alfvén (DKA) vortices8,9—in the Earth's magnetospheric cusp region. As is the case for the larger Kelvin–Helmholtz vortices observed previously17, these dynamic structures should provide a channel for transporting plasma particles and energy through the magnetospheric boundary layers.

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Figure 1: Location of the Cluster spacecraft and the Earth's magnetic field lines.
Figure 2: Proton flux, density and low frequency fields for a cusp passage.
Figure 3: Magnetic field data from the Cluster satellites.
Figure 4: Analytical DKA vortex solution and a vortex model for the turbulence in the cusp.


  1. 1

    Frisch, U. Turbulence: The Legacy of A.N. Kolmogorov (Cambridge Univ. Press, Cambridge, 1995)

    Book  Google Scholar 

  2. 2

    Petviashvili, V. I. & Pokhotelov, O. A. Solitary Waves in Plasmas and in the Atmosphere (Gordon and Breach Science Publishers, Philadelphia, 1992)

    MATH  Google Scholar 

  3. 3

    Horton, W. & Hasegawa, A. Quasi-two-dimensional dynamics of plasmas and fluids. Chaos 4, 227–251 (1994)

    ADS  Article  Google Scholar 

  4. 4

    Pokhotelov, O. A., Stenflo, L. & Shukla, P. K. Nonlinear structures in the earth's magnetosphere and atmosphere. Plasma Phys. Rep. 22, 852–863 (1996)

    ADS  Google Scholar 

  5. 5

    Horton, W. Drift waves and transport. Rev. Mod. Phys. 71, 735–778 (1999)

    ADS  Article  Google Scholar 

  6. 6

    Shukla, P. K., Yu, M. Y. & Varma, R. K. Formation of kinetic Alfvén vortices. Phys. Lett. A 109, 322–324 (1985)

    ADS  Article  Google Scholar 

  7. 7

    Petviashvili, V. I. & Pokhotelov, O. A. Dipole Alfvén vortices. JETP Lett. 42, 54–56 (1985)

    ADS  Google Scholar 

  8. 8

    Shukla, P. K., Yu, M. Y. & Stenflo, L. Electromagnetic drift vortices. Phys. Rev. A 34, 3478–3480 (1986)

    ADS  CAS  Article  Google Scholar 

  9. 9

    Liu, J. & Horton, W. The intrinsic electromagnetic solitary vortices in magnetized plasma. J. Plasma Phys. 36, 1–24 (1986)

    ADS  Article  Google Scholar 

  10. 10

    Burlaga, L. F. A heliospheric vortex street. J. Geophys. Res. 95, 4333–4336 (1990)

    ADS  Article  Google Scholar 

  11. 11

    Zhou, Y., Matthaeus, W. H. & Dmitruk, P. Magnetohydrodynamic turbulence and time scales in astrophysical and space plasmas. Rev. Mod. Phys. 76, 1015–1035 (2004)

    ADS  Article  Google Scholar 

  12. 12

    Hones, E. W. et al. Further determination of the characteristics of magnetospheric plasma vortices with ISEE 1 and 2. J. Geophys. Res. 86, 814–820 (1981)

    ADS  Article  Google Scholar 

  13. 13

    Chmyrev, V. M. et al. Alfvén vortices and related phenomena in the ionosphere and the magnetosphere. Physica Scripta 38, 841–854 (1988)

    ADS  Article  Google Scholar 

  14. 14

    Chmyrev, V. M. et al. Vortex structures in the ionosphere and magnetosphere of the earth. Planet. Space Sci. 39, 1025–1030 (1991)

    ADS  Article  Google Scholar 

  15. 15

    Stasiewicz, K. et al. Small scale Alfvénic structure in the aurora. Space Sci. Rev. 92, 423–533 (2000)

    ADS  Article  Google Scholar 

  16. 16

    Savin, S. et al. Turbulent boundary layer at the border of geomagnetic trap. JETP Lett. 74, 547–551 (2001)

    ADS  Article  Google Scholar 

  17. 17

    Hasegawa, H. et al. Transport of solar wind into Earth's magnetosphere through rolled-up Kelvin-Helmholtz vortices. Nature 430, 755–758 (2004)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Spolaore, M. et al. Vortex-induced diffusivity in reversed field pinch plasmas. Phys. Rev. Lett. 93, 215003 (2004)

    ADS  CAS  Article  Google Scholar 

  19. 19

    Escoubet, C. P., Schmidt, R. & Goldstein, M. L. Cluster—science and mission overview. Space Sci. Rev. 79, 11–32 (1997)

    ADS  Article  Google Scholar 

  20. 20

    Weiland, J. Collective Modes in Inhomogeneous Plasma (IoP Publishing, Bristol, 2000)

    Google Scholar 

  21. 21

    Sundkvist, D. et al. Multi-spacecraft determination of wave characteristics near the proton gyrofrequency in high-altitude cusp. Ann. Geophys. 23, 983–995 (2005)

    ADS  Article  Google Scholar 

  22. 22

    Samson, J. C. Some comments on the descriptions of the polarization states of waves. Geophys. J. R. Astr. Soc 61, 115–129 (1980)

    ADS  Article  Google Scholar 

  23. 23

    Volokitin, A. S. & Dubinin, E. M. The turbulence of Alfvén waves in the polar magnetosphere of the earth. Planet. Space Sci. 37, 761–765 (1989)

    ADS  Article  Google Scholar 

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The authors thank the FGM, EFW and CIS Cluster instrument teams for supplying data for this study. Gratitude goes to T. D. de Wit for his help with the wavelet calculations. The research of D.S., V.K. and P.K.S. was partially supported by the European Commission. The research of A.V. was supported by the Swedish Research Council.

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Correspondence to David Sundkvist.

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Sundkvist, D., Krasnoselskikh, V., Shukla, P. et al. In situ multi-satellite detection of coherent vortices as a manifestation of Alfvénic turbulence. Nature 436, 825–828 (2005).

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