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Turbulence in the Earth's plasma sheet

The Physics of Solar-Wind/Magnetosphere Coupling November 4-8, 2006 Fiesta Americana Hotel, Puerto Vallarta, Mexico. Turbulence in the Earth's plasma sheet. Z. Vörös , W. Baumjohann, R. Nakamura, M. Volwerk, A. Runov Space Research Institute, Graz, Austria

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Turbulence in the Earth's plasma sheet

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  1. The Physics of Solar-Wind/Magnetosphere CouplingNovember 4-8, 2006Fiesta Americana Hotel, Puerto Vallarta, Mexico Turbulence in the Earth's plasma sheet Z. Vörös, W. Baumjohann, R. Nakamura, M. Volwerk, A. Runov Space Research Institute, Graz, Austria Acknowledgements: Y. Asano,T. Nagai (Tokyo Institute of Technology, Japan), T. Mukai (Institute of Space and Astronautical Science, Japan), E. Lucek (Imperial College, London, UK), H. Rème (CESR/CNSR, Toulouse, France).

  2. OUTLINE non-properties • The effect of transient driving on: (non-stationarity) • - spectral indices in plasma sheet turbulence • - spectral break • Multi-scale coupling. How does it work? • -local interactions (non-linearity) • -nonlocal interactions (non-universality) • (non-extensivity) • The effect of the local mean magnetic field • -spectral anisotropy (anisotropy) • -2D turbulence • Fluctuations near magnetic reconnection

  3. Spectral scaling Plasma sheet Solar wind (Hoshino et al. 1994; Bauer et al. 1995; Borovsky& Funsten, 1997, 2003; Vörös et al., 2003, 2004, 2005; Volwerk et al., 2003; Weygand et al., 2005) (Bavassano et al., 1982; Bruno and Carbone, 2005) 1~ 0.5  1.5 2 ~ 1.7  2.9 Inertial range:  ~ 1.7

  4. Transient driving – a sliding window studyCLUSTER alfaest_01Aug27_out • P(f) ~ cf f - • (scale, time) = (2j, 2j t) • j =(1/nj)tnj dx2 (j,t) • ~ 2j cf • Logscale diagram: •  and cf are estimated from • yj  log2 j versus j =log22j

  5. Transient driving – a sliding window studyGEOTAIL

  6. Spectral scaling within individual flows Selection criteria: Bx < 15 nT; <V> > 250 km/s; Small-scale activity. B T_gp [nT] [s] ======== 5 13 10 7 15 4 Dissipation range Inertial range

  7. Large-scale average velocity vs. dissipation scale As a flow energy (~V2 ) increases, the dissipation time scale decreases (coupling)  more energy pumped towards small-scales.  The spectral break depends on both large scale energy input and proton gyroperiod V~80 km/s V~700 km/s Spectral widening + Doppler effect <V> [km/s] Vörös et al., 2005

  8. Multiple flow smearing C with O M M F P U L A L O R T W I I S S P O L N E Individual flows Multiple flows: (a) smear the break; (b) hide the inertial range scaling. Reconnection related?

  9. Local flows vs. multiple flows - kurtosis Local flow Non-flow interval Multiple flows reconnection related?

  10. Nonlocal interactions I Experimental evidence: When a large scale scalar gradient is imposed on a turbulent velocity field, the resultant small scale scalar fluctuations reflect the large scale gradient. The small scales are not universal (Tong & Warhaft, 1994; Warhaft, 2000), the PDFs are skewed. Numerical simulations: Turbulent mixing makes the scalar gradient field patchy. As a consequence, anisotropy induces intermittency (Holzer & Siggia, 1994). Scalar contaminant in a turbulent flow: Skewness and kurtosis plot collapses onto a quadratic curve (Chatwin, Robinson, 1997). Kurtosis Skewness

  11. Nonlocal interactions II - analogy Scalar contaminant in a turbulent flow (advection-diffusion equation): Magnetic field fluctuations in MHD • v is the turbulence velocity; • is the magnetic diffusivity. The equation for the magnitude B =Bn (x,t) is the concentration of passive scalar; Kis the molecular diffusivity; Y(x,t) is the random (turbulent) velocity, which satisfies the Navier-Stokes eq. and mass conservation. The statistical properties of the magnitude B in MHD flows resemble, in the inertial range, those of passive scalars in fluid turbulence (Bershadskii & Sreenivasan, 2004)

  12. Spatial structure of turbulence: multi-point Cluster (non-local interactions) Possible flow geometry 3700 km

  13. Skewness and Kurtosis 1 1 2 2 3 3 4 4

  14. Comparisons Kurtosis Passive scalar statistics in a fluid flow (Chatwin, Robinson, 1997) Skewness Passive scalar statistics near interplanetary shocks (Vörös et al., 2006a) Vörös et al., 2006b Passive scalar statistics in the Earth’s plasma sheet (this study) Evidence for non-local turbulence Interactions. Boundary flows …. Non-boundary flows ….

  15. Anisotropy Large eddies are almost isotropic; Smaller eddies are anisotropic and they are elongated along the local mean magnetic field and not along the global meanB; The local mean field is not the same for the large eddies and the small eddies  scale-dependent anisotropy Real space structure of turbulent eddies Cho et al., ApJ, 2002 We do not know the structure of the eddies in the plasma sheet (if they exist at all…); Speculation: Magnetic fluctuations at a given scale “feel” a local mean field at a scale which is of an order larger; e.g. fluctuations at the time scale of 0.3 s feel the local mean field at 3 s.

  16. Anisotropy Vörös et al., JGR, 2004; Vörös et al., Phys.Plasmas, 2004; Time scale: 0.3 s Time scale: 1.3 s Magnetic fluctuations exhibit scale-dependent anisotropy – the perpendicular power becomes larger than the parallel power  2D turbulence

  17. Example: reconnection and bursty flows on 2001-10-01 (Runov et al., 2003) • High correlation • between the • large-scale magnetic • field measurements; • What about the • high-frequency • (meso-/small-scale) • fluctuations ? • Multi-scale • description is needed?

  18. Hoshino et al. 2001 C1 C2 C4 C3 Nagai et al., 2001 Baumjohann & Nakamura, 2006 B A C B V Quadrupolar Hall magnetic field Runov et al., 2003 BY Bx

  19. C1 Borg et al. 2005 Z Angle between Earthward direction and B and V EZ B EY VxB V EX X C4 • Hall EZchanges direction; • Large Ex,y are associated with • density minima. C3 Tail Earth C4 Earth Tail C1 C4 C3

  20. C1 18 s UT meanf1_isra.m C A B olvas_mind4.m

  21. C3 A B C

  22. C4 A B C

  23. B C A Time C1 C C1 B C1 A C2 C C2 B C2 A C3 C C3 B C3 A C4 C C4 B C4 A

  24. B C A C1 C C1 B C1 A C2 C2 C2 C B A C3 C C3 B C3 A C4 C C4 B C4 A

  25. Conclusions • Turbulence is transient in the plasma sheet; • Multiple flows or badly chosen intervals mask the true inertial range scaling index, which is  ~ 1.7; • The ‘dissipation range’ is well visible from high-resolution magnetic data Scaling index:  ~ 2.6; • Boundary effects and non-local coupling discernible from 4-point Cluster; • Hall structures near reconnection region identified ; • Anisotropic fluctuations within the diffusion region • – effect of the currents, energy injection or local mean field?

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