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Z. V örös University of Innsbruck, Austria Acknowledgements:

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## Z. V örös University of Innsbruck, Austria Acknowledgements:

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**Multi-scale complexity**in space physics FWF Project Support • Z. Vörös • University of Innsbruck, Austria • Acknowledgements: • Runov (Los Angeles), T.L. Zhang (Graz), W. Baumjohann (Graz), M. Volwerk (Graz), • M. Delva (Graz), R. Nakamura (Graz), V. Angelopoulos (Los Angeles), • G. Zimbardo (Calabria), H. Reme (Toulouse), E.A. Lucek (London), • M.P. Leubner (Innsbruck), E. Yordanova (Uppsala) and R. Bruno (Rome) TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**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; • COMPLEXITY COMPLEXITY2 TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**MOTIVATION - OUTLINE**• Turbulence, magnetic reconnection, system-wide dynamical responses in the Earth´s magnetosphere; • Turbulence, structures, magnetic reconnection in the solar wind; TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**Earth‘s magnetosphere**Understanding turbulence is important because it influences the transport of mass, momentum, and energy from the solar wind to the magnetosphere. Turbulence also influences the equilibrium structure of the magnetosphere and the plasma dynamics and energization at many locations. TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**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 TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**Turbulence in the magnetosphere**Borovsky Hasegawa et al. Nature, 2004 Plasma sheet Shock assoc. Cusp Magnetosheath K-H boundary layer TURBULENCE IN THE MAGNETOSPHERE TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**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 TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**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 TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**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 TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**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 TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**BBF associated turbulence**Scaling region, scaling index, Reynolds number, all depend on the <bulk speed>. Doppler shift + spectral widening spectral widening TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**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 TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**Individual vs. multiple flows**Independent driving sources Individual flows: stationary Multiple flows: mixed, non-stationary TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**Check of Taylor hyp. : temporal vs. spatial**TWO-POINT Spatial fluctuations between Cluster 1,4: ONE-POINT Time-delayed fluctuations: (Vörös et al. 2006) TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**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 TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**CLUSTER**THEMIS**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**Large-scale topological changes preceeding reconnection**Laitinen et al., 2007 Sudden changes in B direction at the positions of Cluster and Goes dipolarization TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**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 TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**THEMIS results**Angelopoulos et al., 2008 TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**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??**Multi-scale complexity in the magnetosphere**• OBSERVATIONS INDICATE: • There exist reconnection associated turbulent • fluctuations between MHD and kinetic • scales from a few RE down to tenth of kms; • Turbulent fluctuations can support or stop reconnection; • 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. TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**The solar wind**Heating of the solar wind Adiabatic expansion (no heat is transferred to or from the fluid) • Solar wind plasma is cooling down while it is blown away from the sun • more slowly than it is expected from an adiabatic spherical expansion • Heating is needed to explain the observed temperature radial profile. (Leamon, 1999) Both turbulence and magnetic reconnection can heat the solar wind (Carbone et al. 2009; Retino et al., 2007; Gosling, 2008). TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**Turbulence in the solar wind**(Belcher and Davis, 1971) Nonlinear interactions (Bruno, Carbone, 2005) Alfvenic turbulence Contrapropagating modes are needed! Inertial range scaling shows scaling index typical for isotropic hydrodynamic turbulence. TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**Scaling laws in the SW**Large-scale fluctuations are weakly stationary (Mattheaus &Goldstein, 1982) Large-scale structures Interaction Turbulence However: the interaction between large-scale structures and turbulence is largely unexplored and ignored… mesoscale turbulence IS NOT stationary. TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**Complexity in the solar wind**Since the Sun variably emits a mixture of streams and transient ejecta, a single mechanism cannot reproduce all the complexity associated with turbulence in the solar wind (Bruno and Carbone, 2005). The complex structure of heliospheric current sheet observed by multi-spacecraft data analysis (Foullon et al., 2009) The presence of a mixture of different plasma populations largely contained in separated flux tubes, multi-scale structures, gradients and boundaries is the rule rather than exception. TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**FLUX TUBES VS. TURBULENCE**• B fluctuates around • the <B> direction within • a flux tube; • discontinuities between • the flux tubes affect • turbulence statistics Borovsky, 2008 Bruno et al., 2004 TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**Shocks and turbulence in the solar wind**Vörös et al. 2010 TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**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 TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**RECONNECTION IN THE SW**• Gosling, 2007, 2009 • Phan et al., Nature, 2006 • 1.) Reconnection is frequent in the SW • 40-70 events/month at 1 AU 2.) How does the reconnection X line become so extended?? Perhaps it starts in a limited region closer to the Sun, then spreads? TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**RECONN. JETS AND TURBULENCE**TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**RECONNECTION CLOSER TO THE SUN**How does the reconnection X-line become so extended? Can magnetic reconnection start closer to the Sun in a limited region and spread with time? Venus Express (at 0.72 AU) spends majority of ist orbit, ~ 20 hours per day, in the solar wind (Zhang et al., 2008). ++++ 4 years of magnetic data from VEX - - - - - plasma moments are not routinely available TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**A MAGNETIC HOLE AT 0.72 AU**Venus Express • B 0 nT • embedded in a smoothly increasing B during the day; • large directional • changes of the magnetic field vector; • enhanced magnetic • power. Magnetic depth Wavelet power TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**FLUX TUBE SIGANTURES**Sun X Z Y VEX TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**TURBULENCE IN THE FLUX TUBES**• P(f) ~ c.f - • - scaling index Q- goodness of the fit; Q>0.05 =1.59 Q=0.73 Wavelet power Bx Octave 4-400s time scale TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**TURBULENCE IN THE FLUX TUBES** Q Q Bx By Bz Values within a flux tube 1.59 0.73 1.76 0.2 1.27 0.22 1.5 0.003 1.59 0.58 1.5 0.008 Values within more than one flux tube TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**TURBULENCE IN THE FLUX TUBES** Q Q Bx By Bz Values within a flux tube 2.1 0.96 1.6 0.53 1.6 0.0007 0.86 0.9 2.0 0.43 1.67 0.58 Values within more than one flux tube TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**AND…**• How the flux tube associted turbulence can be • important for the observations of magnetic reconnection? TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**WAVELET COHERENCE**MR dissipation region? Outside the dissipation region magnetic field is ‘frozen-in’. Plasmas in different flux-tubes do not mix. Flux-tubes with different plasma populations and mean B support different type of Alfvenic (?) fluctuations. Fluctuations in phase and antiphase are symmetric relative to the X line Bx--By By--Bz TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**SIMPLIFYING QUESTIONS**• What is the orientation of the reconnection • associated current sheet? • Can we understand reconnection in 2D? TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**MINIMUM VARIANCE ANALYSIS**Supposing 1-D boundary, the eigenvector corresponding to the smallest eigenvalue computed from the covariance matrix of magnetic field is taken as the boundary normal 8.6 12 14 0.42 0.26 3.5 0.076 0.14 0.6 0.07 0.011 0.1 0.0013 0.0005 0.009 0.009 0.001 0.009 0.63 0.52 0.02 0.17 -0.4 0 -0.17 -0.46 0.980.970.90.82 0.760.71 0.18 -0.2 0.16 0.57 Z Z Y Y Y Y eigenvalue eigenvector boundary normal Current sheet normal directions change from Z to Y TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**2D HALL RECONNECTION**Current sheet normal (Z) Hoshino et al. 2001 +Bx Nagai et al., 2001 Magnetic field -Bx C2 C1 Speed C4 C3 By By + + - - + - + - Bx Bx TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**RECONNECTION GEOMETRY**Y (current sheet normal) Z Y X ???? X Z Possible 2D reconnection planes: a.) X-Y b.) Y-Z c.) between a.) and b.) TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**2D Reconnection in Y-Z plane**-Bz X Z X +Bz X Y normal to Y normal to Z The out-of-plane Hall component is Bx. + - - - ++ + - TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**Reconnection jets**V Vz Vx Vy Data provided by J-A. Sauvaud, R. Lundin, E. Penou, A. Fedorov, A. Opitz V TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria**CONCLUSIONS**• TURBULENCE IN THE SOLAR WIND SHOULD BE • ANALYZED WITHIN FLUX TUBES OR ASSOCIATED • WITH MAGNETIC STRUCTURES, DISCONTINUITIES; • HALL RECONNECTION SIGNATURES OBSERVED AT • 0.72 AU (VEX) IN THE SOLAR WIND; • SIGNATURES OF MULTI-SCALE EVOLUTION AND • COMPLEXITY TROMSO-2010 Vörös: Multi-scale complexity, University of Innsbruck, Austria