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Z. Vörös (1) In collaboration with:

Multi-scale statistics associated with plasma flows and magnetic reconnection in the Earth’s plasma sheet. Complexity in plasma and geospace systems University of Tromso, Geilo, Norway, 2007. Z. Vörös (1) In collaboration with:

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Z. Vörös (1) In collaboration with:

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  1. Multi-scale statistics associated with plasma flows and magnetic reconnectionin the Earth’s plasma sheet Complexity in plasma and geospace systems University of Tromso, Geilo, Norway, 2007 Z. Vörös (1) In collaboration with: W. Baumjohann (1), R. Nakamura (1), M. Volwerk (1), A. Runov (1), Y. Asano (1), T. Takada (1), A. Balogh (2) and B. Klecker (3) (1)Space Research Institute, Graz, Austria, (2)Imperial College, London, UK, (3)Max-Planck-Institut für extraterrestrische Physik, Garching, Germany

  2. OUTLINE • Transiency of multi-scale turbulence in the Earth’s plasma sheet; • How to detect turbulence in the plasma sheet; • Magnetic reconnection associated fluctuations; • Spectral anisotropies associated with local mean magnetic field; • Anisotropy and intermittency associated with flow boundaries.

  3. The multi-scale nature of turbulence In the Earth’s plasma sheet (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) In the solar wind (Bavassano et al., 1982; Bruno and Carbone, 2005) 1~ 0.5  1.5 ; Inertial range: 2 ~ 1.7  2.9 ? Inertial range scaling index ~ 1.7

  4. Transiency of turbulence in the Earth’s plasma sheet Wavelet analysis in a sliding window (Vörös et al., 2004) Fluctuations are not steady

  5. GEOTAIL shows the same transiency Turbulence is multi-scale: Large-scale driver + inertial range + small scale dissipation Therefore: stationarity of fluctuations has to be required over both large-scales and small-scales;

  6. The true scaling regimes in the plasma sheet • Below the proton gyroperiod (~5-15 s) a new scaling regime appears with spectral index  ~ 2.6; • Multiple flow scaling over time scale larger than ~ minutes indicate contribution from independent sources (e.g. multiple reconnection)

  7. The inertial range of turbulence in the plasma sheet might be hidden due to multiple flow smearing; and as a consequence, wide range of values for the scaling indices were observed by different authors.

  8. Substorm thin current sheet associated magnetic fluctuations

  9. Sliding window analysis of spectral properties: C3 Over the scales: -- Large Scales (LS): 0.5 – 1.5 [s] -- Small Scales (SS): 0.1 – 0.4 [s]

  10. Magnetic reconnection on August 24, 2003

  11. Dynamic spectra Bx By Bz

  12. Magnetic reconnection associated flows and the Hall current system Bx>0 - Bx=0 Bx<0 Y Cluster traject. Nagai et al., 2001 Earthward Tailward Bx=0 Bx=0

  13. Sliding window analysis of spectral properties: C3 Over the scales: -- Large Scales (LS): 0.5 – 1.5 [s] -- Small Scales (SS): 0.1 – 0.4 [s]

  14. Sliding window analysis of spectral properties: C3 Over the scales: -- Large Scales (LS): 0.5 – 1.5 [s] -- Small Scales (SS): 0.1 – 0.4 [s] ? Turbulence Noise

  15. Sliding window analysis of spectral properties: C4 Over the scales: -- Large Scales (LS): 0.5 – 1.5 [s] -- Small Scales (SS): 0.1 – 0.4 [s] ? Turbulence Noise

  16. Particle time-energy spectrograms C4 - CODIF C3 - HIA Tailw. Earthw. Tailw. Earthw. Tailward bulk flow Tailward bulk flow Earthward bulk flow Particle streams Particle streams

  17. Flow after Nakamura et al., 2004 • Well defined bulk flow; • Inside the plasma flow; • Spectral signatures: • -LS, SS spectral index ~ 2.5; • -enhanced power; • -anisotropies (?) • Patchy particle flux distribution; • Close to PSBL; Bx~0; Bz strongly fluct. • Spectral signatures: • -LS, SS spectral index not equal; • - power fluctuates but not • enhanced.

  18. Spectral anisotropy Real space structure of turbulent eddies 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 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;

  19. Spectral anisotropy in k space Perpendicular spectral transfer is enhanced in the presence of strong local mean magnetic field Bo. The degree of spectral anisotropy can be measured by anisotropy angle (Shebalin et al. 1983): where k is the Fourier wavevector with components parallel and perpendicular to Bo , and the summations extend over all retained wavevectors. Three special cases: 90 o for fully perpendicular; 0 o for fully parallel; 54 o for isotropic fluctuations. Oughton et al. (1998) have shown:  can be estimated from the magnetic field measur. within:

  20. (Scale dependent) spectral anisotropy

  21. Conclusions • The inertial range of turbulence in the plasma sheet might be hidden due to multiple flow smearing; • Magnetic turbulence exhibits a „kinetic“ scaling regime below the proton gyroperiod with spectral index  ~ 2.6; • Local mean magnetic field introduces anisotropy; • Reconnection associated magnetic fluctuations are • significantly different from substorm thin current sheet • associated fluctuations;

  22. Anisotropy and intermittency in higher order statistics PDF

  23. Anisotropy and intermittency Experimental evidence: When a large scale scalar gradient is imposed on a turbulent velocity field, the resultant small scale temperature 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

  24. Spatial structure of turbulence MULTI – POINT CLUSTER (Voros, 2007) Possible flow geometry 3700 km rrr_pos_out.fig

  25. Effect of scalar gradients on skewness and kurtosis II 1 1 2 2 3 3 4 4

  26. Boundary vs. non-boundary flow statistics in the Earth’s plasma sheet Scales: 1.5 -5 s Kurtosis vs. Skewness plot seems to collapse onto a quadratic curve, resembling passive scalar statistics in fluid turbulence.

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