Some features of turbulent processes in the earth’s magnetosphere from the CLUSTER mission measurements

1Kozak, LV, 2Savin, SP, 3Lui, AT, 1Tsupko, OO
1Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
2Space Research Institute of the Russian AS, Moscow, Russia
3Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland, USA
Kosm. nauka tehnol. 2012, 18 ;(2):43–54
Publication Language: Ukrainian
Statistical features of magnetic field fluctuations in bound regions of the Earth’s magnetosphere are investigated on different time scales. The Cluster-2 mission measurements made during 2004—2009 are used for our analysis. Changes in the shape and parameters of probability density function for the magnetic field fluctuations are studied for the time intervals when the satellite was within the magneto-layer, solar plasma wind and magnetopause region. The evolution of the change of the probability density function maximum and kurtosis values are considered and structure functions of different orders are investigated as characteristics of turbulent processes for different time scales. Two asymptotic modes of the change in the maximum height for the probability density function are found which can be described with the use of different power lows. On the basis of the investigation of structure functions of high orders (up to the ninth order), the character of turbulent processes is determined and diffusion in the regions under consideration is studied. It is found that the type of the turbulent processes in the solar wind plasma differ greatly from one in the magneto-layer. Besides, super-diffusion is revealed in transitional regions of the Earth’s magnetosphere.
Keywords: Earth's magnetosphere, magnetic field fluctuations, mission Cluster, solar wind
1. Barenblatt G. I. Turbulent boundary layers at very large Reynolds numbers,  Uspehi mat. nauk, 59, N1(355), 45—62 (2004) [in Russian].
2. Zaks L. Statistical estimation, 598 p. (Statistika, Moscow, 1976) [in Russian].
3. Zaslavskij G. M., Sagdeev R. Z. Introduction to nonlinear physics. From the pendulum to turbulence and chaos, 368 p. (Nauka, Moscow, 1988) [in Russian].
4. Iroshnikov P. S. On the turbulence of a conducting fluid in a strong magnetic field, Astron. zhurn., 40 (4), 742—750 (1963) [in Russian].
5. Kadomcev B. B. Turbulence plasma.   Plasma Physics Questions, Ed. by M.A. Leontovich, 188—339 (Atomizdat, Moscow, 1964) [in Russian].
6. Kadomcev B. B. Collective phenomena in plasma, 303 p. (Nauka, Moscow, 1988) [in Russian].
7. Kozak L.V. A statistical approach for turbulent processes in the Earth ’s magnetosphere from measurements of the satellite Interball.  Kosm. nauka tehnol, 16 (1), 28—39 (2010) [in Russian].
8. Kozak L.V., Pilipenko V.A., Chugunova O.M., Kozak P.N. Statistical analysis of turbulence in the foreshock region and in the Earth's magnetosheath. Cosmic Research, 49 (3), 202—212 (2011) [in Russian].
9. Kolmogorov A. N. The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds' Numbers. Dokl. Academy of Sciences of the USSR, 30(4), 299 — 303 (1941) [in Russian].
10. Zelenyj L.M., Veselovskij I.S. (Eds.) Space geoheliophysics. Vol. 1,  624 p. (Vol. 1-2; Vol. 1) (Fizmatlit, Moscow, 2008) [in Russian].
11. Novikov E. A., Stjuart R. U. The intermittency of turbulence and a range of energy dissipation fluctuations. Bulletin of the Academy of Sciences of the USSR. Geophysics Series, N 3, 408—413 (1964) [in Russian].
12. Savin S.P., Zelenyi L.M., Amata E., et al. Dynamic interaction of plasma flow with the hot boundary layer of a geomagnetic trap.  Journal of Experimental and Theoretical Physics Letters, 79 (8), 452—456 (2004) [in Russian].
13. Frisch U. Turbulence. The Legacy of A.N.Kolmogorov, 343 p. (Fazis, Moscow, 1998) [in Russian].
14. Benzi R., Ciliberto S., Tripiccione R., et al. Extended selfsimilarity in turbulent flows,  Phys. Rev. E, 48, P. R29—R32 (1993).
15. Chechkin A. V., Gorenflo R., Sokolov I. M. Generalized fractional diffusion equations for accelerating subdiffusion and truncated Lévy flights, Phys. Rev., 66, 046129, P. 13 (2002).
16. Consolini G., Kretzschmar M., Lui A. T. Y., et al. On the magnetic field fluctuations during magnetospheric tail current disruption: A statistical approach, J. Geophys. Res., 110, P. A07202, (2005)
17. Dubrulle B. Intermittency in fully developed turbulence: Log-Poisson statistics and generalized scale covariance,  Phys. Rev. Lett., 73, 959—962 (1994).
18. Kraichnan R. H. The structure of isotropic turbulence at very high Reynolds numbers,  J. Fluid Mech., 5, 497—543 (1959).
19. Kraichnan R. H. Lagrangian — history closure approximation for turbulence,  Phys. Fluids, 8, 575—598 (1965).

20. Kraichnan R. H. Convergents to turbulence functions, J. Fluid Mech., 41, 189—217 (1970).

21. Lovejoy S., Schertzer D., Silas P. Diffusion in One Dimensional Multifractal Porous Media, Water Resour. Res., 34, 3283—3291 (1998).
22. Savin S., Amata E., Zelenyi L., et al. High kinetic energy jets in the Earth’s magnetosheath: Implications for plasma dynamics and anomalous transport,  JETP Lett., 87, 593—599 (2008).

23. Shevyrev N. N., Zastenker G. N. Some features of the plasma flow in the magnetosheath behind quasi-parallel and quasi-perpendicular bow shocks,  Planet. and Space Sci., 53, 95—102 (2005).

24. She Z., Leveque E. Universal scaling laws in fully developed turbulence,  Phys. Rev. Lett.,   72, 336—339 (1994).

25. Treumann R. A. Theory of super-diffusion for the magnetopause, Geophys. Res. Lett., 24, 1727— 1730 (1997).