Z. V örös University of Innsbruck, Austria Acknowledgements:

1. Turbulence and intermittency in the Earth‘s magnetotail FWF Project Support • Z. Vörös • University of Innsbruck, Austria • Acknowledgements: • Runov (Los Angeles), T.L. Zhang (Graz), W. Baumjohann (Graz), M. Volwerk (Graz), • R. Nakamura (Graz), V. Angelopoulos (Los Angeles), G. Zimbardo (Calabria), • H. Reme (Toulouse), E.A. Lucek (London), and M.P. Leubner (Innsbruck) Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

2. MOTIVATION - OUTLINE • Dynamical phenomena in space and astrophysical plasmas arise as a consequence of multi-scale energy redistribution, self-organization and instabilities. • Typical multi-scale phenomena in space: turbulence, • magnetic reconnection, multi-scale structures; • STRUCTURES, TURBULENCE AND RECONNECTION • ARE USUALLY NOT INDEPENDENT; Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

3. MOTIVATION - OUTLINE • Turbulence, magnetic reconnection, system-wide dynamical responses in the Earth´s magnetosphere; Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

4. Turbulence in the magnetosphere Re=VL /  Rm=VL/ V L Fully developed turbulence: Re~> 104 Numbers estimated by Borovsky et al., 1997 and Borovsky & Funsten, 2003; supposing e.g. for Re that the kinematic viscosity  can be obtained from Coulomb collisions Re=VL /  ~ 1011 Rm=VL/ ~ 1013 The average rate of energy dissipation per unit mass <> can be determined from large scale quantities: kinetic energy of the large eddies, V2, and lifetime of the eddy, L/V : <> ~ V3/ L The smallest scale S in a cascade: S ~ (3/ <>)1/4 L / S ~ (Re)3/4 Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

5. Scaling and SOC in the magnetosphere Chaos & fractality (Baker et al., 1990; Vörös, 1990; Shan et al, 1991; Roberts et al., 1991; Lui, 1991; Consolini, 1996, etc.) Self-organization (Chang, 1992; Vörös, 1991; Consolini, 1997, 2001; Chapman et al., 1998, 1999; Klimas et al, 1992; 1996,1997; Watkins et al., 2000; Uritsky et al., 2002; Valdivia et al., 2005;etc.) Borovsky Hasegawa et al. Nature, 2004 Plasma sheet Shock assoc. Cusp Magnetosheath K-H boundary layer TURBULENCE & SELF-ORGANIZATION IN THE MAGNETOSPHERE Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

6. Turbulent spectra: geospace Downstream of the bow shock Alexandrova et al., 2004 slope:1.66 Cusp region Nykyri et al. 2006 slope:4.9 slope:2.4 Plasma sheet Volwerk et al., 2004 slope:3.5 slope:2.5-2.7 Magnetosheath Downstream of QP bow shock Yordanova et al., 2008 Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

7. Spectral scaling • Different scalings in different regions of the magnetosphere: • spectral indices • break/no break in the spectra • All the spectra were obtained by the CLUSTER s/c. • The differences in scalings can arise due to: • fits over different frequency ranges • break of Taylor frozen-in hypothesis • non-stationarity • different boundary conditions • different physics Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

8. Turbulence in the plasma sheet Walker et al., Space Sci.Rev., 1999 ~ 30-50 RE Bursty Flow 1-3RE e.g. Hughes, 1995; in K&R e.g. Kivelson & Russel, Intro to Space Physics,1995 Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

9. Turbulence in the plasma sheet Bursty bulk flow associated turbulence: The spatial extent of turbulent flows is: L=1-3 RE (Nakamura et al. 2004). The smallest scale of the fluctuations is the ion gyroscale: S=hundreds of kms. The Reynolds number Re ~ 100 – 1000 turbulence is not fully developed? L / S ~ (Re)3/4 Vörös et al., 2006, Weygand et al, 2007 Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

10. BBF associated turbulence Scaling region, scaling index, Reynolds number, all depend on the <bulk speed>. Doppler shift + spectral widening spectral widening Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

11. Stationarity vs. intermittency Plasma sheet • Multiple flows: • (Intervals A, B) • V ~ (0-1000) km/s; •  ~ (0.5 – 3); • cf ~ (0 – 150); • frequency ↛wavenumber. • Individual flows: • (e.g. interval C) • V ~ 750+- 150 km/s; •  ~ 2.5 +- 0.3; • cf >> 0 ; • frequency  wavenumber. Vörös et al. 2006 Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

12. Individual vs. multiple flows Independent driving sources Individual flows: stationary Multiple flows: mixed, non-stationary Vörös et al. 2006 Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

13. Check of Taylor hyp. : temporal vs. spatial TWO-POINT Spatial fluctuations between Cluster 1,4: ONE-POINT Time-delayed fluctuations: (Vörös et al. 2006) Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

14. Multifractals: multinomial measures A recursive construction rule (Vörös et al. 2003) Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

15. LIM: Local Intermittency Measure (See also Bruno et al., 1999, Consolini & DeMichelis, 2005) f()  The strength of local burstiness (Hölder exponent) (Vörös et al. 2003) Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

16. LIM analysis in the magnetotail (Vörös et al. 2003) Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

17. LIM: cross-scale coupling + dipolarization (Vörös et al. 2003) Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

18. Nonlocal interactions 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). (Vörös et al. 2003) Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

19. Nonlocal interactions and intermittency Possible flow geometry 3700 km (Vörös et al. 2003) Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

20. Skewness and Kurtosis 1 1 2 2 3 3 4 4 (Vörös et al. 2003) Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria Scale [s]

21. Boundary effects in the 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. (Vörös et al. 2007) Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

22. Multi-scale complexity in the magnetosphere • Typical multi-scale phenomena in space: turbulence, • magnetic reconnection, multi-scale structures; • TURBULENCE, MAGNETIC RECONNECTION AND SYSTEM-WIDE RESPONSES ARE NOT INDEPENDENT; • Multi-scale physics = coupling between multiple-scales (not restricted to a turbulent cascade); • System-scale MHD scales kinetic scales (Vörös et al. 2007) Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

23. Reconnection+BBF+ turbulence Hall, two-fluid, eg. Oireoset et al., 2001 Petschek, 1964 Sweet-Parker, 1957 Fast Fast but unstable and not observed Slow Turbulent in 3D Lazarian & Vishniac, 1999 FAST: 1.) collisionless regime 2.) Hall-signatures; 3.) thin current sheet (large-scale reorganization of B) 4.) turbulent B? Fast Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

24. CLUSTER THEMIS

25. CLUSTER MEASUREMENTS Hoshino et al. 2001 C1 C2 C4 C3 Nagai et al., 2001 Z Baumjohann & Nakamura, 2006 B A C B V X Quadrupolar Hall magnetic field Runov et al., 2003 BY By Bx Bx

26. Large-scale topological changes preceeding reconnection Laitinen et al., 2007 Sudden changes in B direction at the positions of Cluster and Goes dipolarization Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

27. Large-scale topological changes preceeding reconnection Laitinen et al., 2007 Sudden changes in B direction at the positions of Cluster and Goes Directional changes of the ambient magnetic field at Cluster Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

28. THEMIS results Angelopoulos et al., 2008 Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

29. Large-scale reconnection signatures Vörös et al., 2009 Strong interaction + flapping Dipolarization Flow reversal Earthward flows+vortices heating Angelopoulos et al., 2008 Does the increase of density stop the reconnection??

30. Multi-scale complexity in the magnetosphere • OBSERVATIONS INDICATE: • There exist reconnection and BBF associated turbulent • fluctuations between MHD and kinetic • scales  from a few RE down to tenth of kms; • Turbulent intermittent fluctuations represent • non-local couplings near boundaries; • Fast reconnection signatures: large-scale • reorganization of the magnetic field (~10 RE), • Hall two-fluid physics – MHD-down to electron scales; • Reconnection jets travel a distance of >~10 RE • and initiate system-wide reorganizations of the • magnetosphere: substorms; • Substorms lead to large-scale reorganizations of B. Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

31. Second-order non-stationarity multiple flows Vörös et al. 2010 single flow Earth‘s magnetosphere Q – goodness of fit measure Q>>0.05 is OK 1 day 2 months Solar wind Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria