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.
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Frisch, U. Turbulence: The Legacy of A.N. Kolmogorov (Cambridge Univ. Press, Cambridge, 1995)
Petviashvili, V. I. & Pokhotelov, O. A. Solitary Waves in Plasmas and in the Atmosphere (Gordon and Breach Science Publishers, Philadelphia, 1992)
Horton, W. & Hasegawa, A. Quasi-two-dimensional dynamics of plasmas and fluids. Chaos 4, 227–251 (1994)
Pokhotelov, O. A., Stenflo, L. & Shukla, P. K. Nonlinear structures in the earth's magnetosphere and atmosphere. Plasma Phys. Rep. 22, 852–863 (1996)
Horton, W. Drift waves and transport. Rev. Mod. Phys. 71, 735–778 (1999)
Shukla, P. K., Yu, M. Y. & Varma, R. K. Formation of kinetic Alfvén vortices. Phys. Lett. A 109, 322–324 (1985)
Petviashvili, V. I. & Pokhotelov, O. A. Dipole Alfvén vortices. JETP Lett. 42, 54–56 (1985)
Shukla, P. K., Yu, M. Y. & Stenflo, L. Electromagnetic drift vortices. Phys. Rev. A 34, 3478–3480 (1986)
Liu, J. & Horton, W. The intrinsic electromagnetic solitary vortices in magnetized plasma. J. Plasma Phys. 36, 1–24 (1986)
Burlaga, L. F. A heliospheric vortex street. J. Geophys. Res. 95, 4333–4336 (1990)
Zhou, Y., Matthaeus, W. H. & Dmitruk, P. Magnetohydrodynamic turbulence and time scales in astrophysical and space plasmas. Rev. Mod. Phys. 76, 1015–1035 (2004)
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)
Chmyrev, V. M. et al. Alfvén vortices and related phenomena in the ionosphere and the magnetosphere. Physica Scripta 38, 841–854 (1988)
Chmyrev, V. M. et al. Vortex structures in the ionosphere and magnetosphere of the earth. Planet. Space Sci. 39, 1025–1030 (1991)
Stasiewicz, K. et al. Small scale Alfvénic structure in the aurora. Space Sci. Rev. 92, 423–533 (2000)
Savin, S. et al. Turbulent boundary layer at the border of geomagnetic trap. JETP Lett. 74, 547–551 (2001)
Hasegawa, H. et al. Transport of solar wind into Earth's magnetosphere through rolled-up Kelvin-Helmholtz vortices. Nature 430, 755–758 (2004)
Spolaore, M. et al. Vortex-induced diffusivity in reversed field pinch plasmas. Phys. Rev. Lett. 93, 215003 (2004)
Escoubet, C. P., Schmidt, R. & Goldstein, M. L. Cluster—science and mission overview. Space Sci. Rev. 79, 11–32 (1997)
Weiland, J. Collective Modes in Inhomogeneous Plasma (IoP Publishing, Bristol, 2000)
Sundkvist, D. et al. Multi-spacecraft determination of wave characteristics near the proton gyrofrequency in high-altitude cusp. Ann. Geophys. 23, 983–995 (2005)
Samson, J. C. Some comments on the descriptions of the polarization states of waves. Geophys. J. R. Astr. Soc 61, 115–129 (1980)
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)
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.
Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests.
About this article
Cite this article
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). https://doi.org/10.1038/nature03931
The Astrophysical Journal (2021)
Journal of Atmospheric and Solar-Terrestrial Physics (2021)
The Astrophysical Journal (2020)
Physica Scripta (2020)
Physical Review X (2019)