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NASA Cluster GI/ RSSW1AU programs

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NASA Cluster GI/ RSSW1AU programs

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  1. Correlation and Anisotropy in solar wind turbulence W H MatthaeusCollaborators: J. M. Weygand, S. Dasso, C. W. Smith, M. G. Kivelson, J. W. Bieber, P. Chuychai, D. Ruffolo, P. TooprakaiBartol Research Institute and Department of Physics and Astronomy, University of DelawareIGPP, UCLAIAFE, Universidad de Buenos Aires, ArgentinaEOS, University of New HampshireMahidol University,Bangkok, THailandChulalongkorn University, Bangkok, Thailand - Turbulence theory - single spacecraft observations - Multispacecraft ACE –Wind-Cluster-Geotail, IMP data NASA Cluster GI/ RSSW1AU programs

  2. VanDyke, An Album of Fluid Motion Mean flow and fluctuations • In turbulence there can be great differences between mean state and fluctuating state • Example: Flow around sphere at R = 15,000 Instantaneous flow Mean flow

  3. Essential properties of turbulence Batchelor and Townsend, 1949 • Complexity in space + time (intermittency/structures) • O(1) diffusion/energy decay • wide range of scales, ~self similarity dE/dt ~ -u3/L K41

  4. Large scale features of the Solar Wind: Ulysses • High latitude • Fast • Hot • steady • Comes from coronal holes • Low latitude • slow • “cooler” (40,000 K @ 1 AU) • nonsteady • Comes from streamer belt McComas et al, GRL, 1995

  5. MHD scale turbulence in the solar wind • Powerlaw spectra cascade • spectrum,  correlation function Magnetic fluctuation Spectrum, Voyager at 1 AU

  6. Single s/c background: frozen-in flow approx. Space-time correlation assume fluctuation undistorted in fast flow U   measured 1 s/c correlation related To 2-point 1-time correlation by this mixes space- and time- decorrelation, and while useful, needs to be verified (as an approximation) and further studied to unravel the distinct decorrelation effects

  7. What multi s/c can tell us • Spatial correlations R(r)  fit, or full functional form • When we have enough samples, R(r,r) • examine frozen-in flow approx. (predictability) • Infer the Eulerian (two time, 1 pt) correlation Problem: We do not have hundreds or thousands of s/c to use. So, we must average two point correlations at different places and times.

  8. Variability, Similarity and PDFs R(r)  Z2 R( r / l ) e.g., for Correlation function ^ Similarity variables: turbulence energy, correlation scale (per unit mass) • Variance is approx. log-normally distributed • v, b fluctuations are approx. Gaussian • Normalization separates these effects  defines ensemble

  9. PDF of component variances • Variances are approx. log-normal  Suggests independent (scale invariant) distribution of coronal sources

  10. PDF of B components at 1AU • When normalized to remove variability of mean and variance, component distributions are close to Gaussian ”primitive fields” are ~Gaussian, but derivatives are intermittent Padhye et al, JGR 2001; Sorriso-Valvo et al, 2001

  11. Mean in interval I Energy interval I Structure function estimate interval I Correlation function estimate interval I

  12. Data: ACE-Wind Geotail-IMP 8 • 1 min data. • 12 hr intervals. • Subtract mean field in interval. • Normalize correlation estimate by observed variance. • ACE-Wind pair separations: ≈ 0.32·106 to 2.3·106 km. • Geotail-IMP 8 pair separations (not shown) : ≈ 0.11·106 to 0.32·106 km. £ 106 £ 106

  13. Data: Cluster Correlations in SW • 22 samples/sec • 1 hr intervals. • 6 separations/interval (4 s/c) • Mean removed, detrended. • Normalize correlation estimate by observed variance. • Black dash: SW intervals. • Blue Dash: plasma sheet intervals. (Weygand SM24A-3)

  14. Solar Wind: 2 s/c magnetic correlation function estimates Cluster in the SW Geotail-IMP 8 ACE-Wind

  15. Correlation scale from Cluster/ACE/Wind/Geotail/IMP8 Correlations Separation (106 km) c = 1.3 (±0.003) £ 106 km

  16. Taylor microscale scale T • Determine Taylor scale from Taylor expansion of two point correlation function: • Need to extract asymptotic behavior, need fine resolution Richardson extrapolation • Result is: • T = 2400 ± 100 km

  17. SW Taylor Scale Taylor Scale: Least Squares Fit • Estimate lT from quadratic fits to S(r) with varying max. separation • Linear fit to trend of these estimates from 600 km to r-max for every r-max. • Extrapolate each linear fit to r=0 (call this a refined estimate of T) • Look for stable range of extrapolations lT stable from about 1,000 to 11,000 km.  Value is lTS = 2400 ± 100 km ¼3.4 ion gyroradii • Ion gyroradius est. ≈700 km. • Ion inertial length est. ≈100 km. Taylor Scale (least Sq. Fit) Ion gyrorad. 2.9 5.7 8.6 11.4 14.2 17.1 2.9 5.7 8.6 11.4 14.2 17.1 lTS: 2400 ± 100 km Taylor Scale (linear Fit)

  18. 2-spacecraft two point, single time correlations of SW turbulence • correlation (outer, energy-containing) scale c = 1.3 £ 106 km, ~ 190 Re ~ 0.008 AU • inner (Taylor) scale • lTaylor= 2400 km ~ 1.6 £ 10-5 AU • another scale: Kolmogoroff or “dissipation scale” d is termination of inertial range Effective Reynolds number of SW turbulence is (Lc/lT)2¼ 230,000

  19. Comparison of correlation functions from 1 s/c (frozen-in) measurements, and 2 s/c (single separation) measurements • Two Cluster samples • give • two 1 s/c estimates of R(r) for a range of r •  one 2 s/c • estimate of R(r) • R= s/c separation 2 s/c 1 s/c 1 s/c 2 s/c 1 s/c 1 s/c Deviation from frozen-in flow is a measure of temporal decorrelation, i.e., connection to Eulerian single point two time correlation fn  in progress)

  20. Spectral Anisotropy

  21. Anisotropy in MHD associated with a large scale or DC magnetic field Shebalin, Matthaeus and Montgomery, JPP, 1983

  22. Preferred modes of nearly incompressible cascade • Low frequency quasi-2D cascade: • Dominant nonlinear activity involves k’s such that Tnonlinear (k) < TAlfven (k) • Transfer in perp direction, mainly • k perp >> k par • Resonant transfer: Shebalin et al, 1983 • High frequency Z+ wave interacts with ~zero frequency Z- wave to pump higher k? high frequency wave of same frequency • Weak turbulence: Galtier et al See: two time scale derivation of Reduced MHD (Montgomery, 1982)  All produce essentially perpendicular cascade!

  23. Cross sections dB/B0 = 1/10 Jz and Bz in an x-z plane Jz and Bx, By in an x-y plane

  24. Solar Wind  Quasi-Perpendicular cascade…..plus “waves” B0

  25. Maltese cross • Several thousand samples of ISEE-3 data • Make use of variability of ~1-10 hours mean magnetic field relative to radial (flow) direction Quasi-2D r ‖ Quasi-slab r┴

  26. Magnetic field autocorrelation SLOW SW: More 2D-like FAST SW: More slab-like r ‖ r┴ <400 km/s > 500 km/s Levels 1000 1200 1400 1600 1800 2000

  27. Correlations in fast and slow wind, as a function of angle between observation direction and mean magnetic field

  28. Spatial structure and complexity Models that are 2D or quasi-2D  transverse structure gives rise to complexity of particle/field line trajectories (non Quasilinear behavior).

  29. 2D magnetic turbulence: Rm=4000, t=2, 10242 Magnetic field lines [contours of a(x,y)] Electric current density

  30. “Cuts” through 2D turbulence bx(y) Analogous to bN(R) in SW magnetic field data. Compare with ~5 day Interval at 1 AU

  31. Magnetic field lines/magnetic flux surfaces for model solar wind turbulence A mixture of 2D and slab fluctuations in the “right” proportion Magnetic structure is spatially complex

  32. IMF with transverse structure and topological “trapping” “core” of SEP with dropouts Piyanate Chuychai, PhD thesis 2005 Ruffolo et al.2004 “halo” of low SEP density over wide lateral region

  33. Orbit of a selected field lines in xy-plane Radial coordinate (r) vs. z

  34. Particle trapping, escape and delayed diffusive transport Tooprakai et al, 2007

  35. Dissipation and Taylor scales: some clues about plasma dissipation processes

  36. steepening near 1 Hz (at 1 AU) -- breakpoint scales best with ion inertial scale Helicity signature  proton gyroresonant contributions ~50% Appears inconsistent with solely parallel resonances kpar and kperp are both involved Consistent with dissipation in oblique current sheets Solar Wind Dissipation Leamon et al, 1998, 1999, 2000

  37. Dissipation scale and Taylor scales (ACE at 1 AU) •  T > d cases are like hydro • T < dcannot occur in hydro, it is a plasma effect. Further study of the relationship between these curves may provide clues about plasma dissipation clouds: red (C. Smith et al)

  38. Summary • Correlation functions • 2 pt 1 time, 1 pt 2 time, predictability • Anisotropy • Incompressible: dominant perp cascade • Low freq quasi 2D + waves • Structure and complexity • Diffusion and topology • Dissipation and Taylor scales • What limits mean square gradients in a plasma?

  39. Activity in the solar chromosphere and corona:SOHO spacecraft Origin of the solar wind UV spectrograph: EIT 340 A White light coronagraph: LASCO C3

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