Vladimir Zhdankin, JILA/CU-Boulder US-Japan Magne>c Reconnec>on Workshop, 3/7/2016

Transcription

1 Vladimir Zhdankin, JILA/CU-Boulder US-Japan Magne>c Reconnec>on Workshop, 3/7/2016 Stanislav Boldyrev (UW-Madison), Dmitri Uzdensky (CU-Boulder), Steve Tobias (U-Leeds), Jean Carlos Perez (FIT) 1

2 I. Introduc>on: intermivent energy dissipa>on in turbulence II. Methodology: sta>s>cal analysis of dissipa>ve structures III. Spa>al analysis: current sheets (spanning many scales) IV. Temporal analysis: flare events (i.e., evolving current sheets) V. Conclusions 2

3 1. Randomness and irreversibility 2. Fluctua>ons over many scales 3. Energy transfer across many scales Energy in at large scales, cascades to small scales, then dissipates Z Solar wind (Sahraoui et al. 2010) v(k) = d 3 xv(x)e ik x E(k) v(k) 2 4 k 2 Kolmogorov 1941: Scale invariance + dimensional analysis -> E(k) k 5/3 3

4 Random fluctua>ons in turbulent cascade cause energy dissipa>on to be inhomogeneous in space and in >me IntermiVency breaks scale invariance: as spa>al resolu>on is increased, quan>>es such as the local energy dissipa>on rate become increasingly inhomogeneous Consequences: non-gaussian sta>s>cs, coherent structures Standard methods (e.g., structure func>ons) have limita>ons - need new, more robust and informa>ve methods Sreenivasan 1999 Kira & Miura 1998 Leung et al

5 IntermiVent structures are sites of localized hea>ng, par>cle accelera>on, magne>c reconnec>on, etc. Vor>city filaments in hydrodynamics, current/vor>city sheets in plasmas Sta>s>cal analysis of intermivent structures is robust methodology for inves>ga>ng dynamics in numerical simula>ons and observa>ons Hydrodynamic turbulence: Jiménez et al. 1993, Moisy & Jiménez 2004, Leung et al MHD turbulence: Servidio et al , Uritsky et al. 2010, Zhdankin et al , Momferratos et al. 2014, Wan et al. 2014, Makwana et al Douady et al

6 2D MHD turbulence: reconnec>on occurs in Sweet-Parker-like current sheets Servidio et al. PRL 2009, PoP 2010 Zoom in on a current sheet... Local reconnec>on rate Major remaining ques>on: how does this change in 3D? 6

7 In 3D reduced MHD turbulence (Zhdankin et al. 2013, Wan et al. 2014): Many current sheets are not associated with X-type null points, and many X-points are not associated with current sheets Most intense current sheets have tendency to include X-point Unclear whether Sweet-Parker model is valid Wan et al. ApJ 2014 Zhdankin et al. ApJ

8 Dynamics governing inhomogeneous dissipa>on in solar corona are poorly understood; self-organized cri>cality and turbulence may play roles Solar flares exhibit power-law distribu>ons for size, dura>on, peak intensity, and energy released E: If α < 2.0, then strongest flares dominate If α > 2.0, then weakest flares dominate (nanoflare hea>ng; Parker 1983) E tot P (E) / E Z Emax E min EP(E)dE E2 max E 2 min 2 P (E) Aschwanden et al Solar flare observa>ons measure α 1.8, making nanoflare hea>ng douboul E 8

9 What is morphology of intermivent structures? (filament, sheet, etc.) What are sizes and dura>ons of dissipa>ve events? How are they related? Is energy dissipa>on dominated by weak or strong (small or large) structures/events? ( coherent structures or nanoflares?) How do results scale in limit of large Reynolds numbers? Do dissipa>ve events exhibit any substan>al temporal asymmetry? Can turbulence explain flares in astrophysical systems? (e.g., corona) To what extent are intermivent current sheets associated with magne>c reconnec>on? To answer these ques>ons, will perform a sta>s>cal analysis of intermivent current sheets in numerical simula>ons of driven MHD turbulence 9

10 Reduced MHD: incompressible MHD in limit of strong uniform background magne>c field and anisotropic gradients: B = B 0 ẑ + b B 0 b rms Valid at scales small rela>ve to driving scale, but large rela>ve to kine>c scales k? k t + v r? = B z + r t! + v r?! b r? j = B z j + r 2?! Periodic box, large-scale driving Pm = =1 b =ẑ r j = r 2? v =ẑ r! = r 2? Compensated magne>c energy spectrum Re = v 0L = B 0 /b rms 5 Dissipa>on rates:, j 2! 2 Details on simula>ons: Perez et al

11 Re = 1000 Re = 3200 Re = 9000 Current density contours in plane perpendicular to guide field 11

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13 Iden>fy 3D intermivent current sheets in each snapshot by applying threshold j thr >j rms and finding sets of connected points with j >j thr j thr 6.4j rms j thr 4.3j rms j thr 2.1j rms For each structure, measure size in 3 direc>ons: Z Also measure energy dissipa>on rate: E = dv j 2 L>W >T 13

14 Energy dissipated in structures Number of structures Volume occupied 50% of resis>ve energy dissipa>on in 3% of s volume E tot Insensi>ve to Re when threshold rescaled to rms: j rms = Re 1/2 V tot 14

15 E = Z dv j 2 Compensated E Power law tail with index very close to cri>cal value of -2.0 Weak and strong structures both contribute equally to overall energy dissipa>on rate Energy dissipa>on is spread across a con>nuum of scales 15

16 Distribu>ons for spa>al scales Length Width Thickness Dissipa>on-weighted distribu>ons for spa>al scales E(X)dX = energy dissipa>on rate from all structures with scale between X and X + dx 16

17 Rescaled dissipa>on-weighted distribu>ons L 2/3 W 2/3 T 2/3 Distribu>ons coincide when rescaled rela>ve to dissipa>on scale Goldreich & Sridhar 1995: l?, 3/4 l k, 1/2 With scale-dependent dynamic alignment (Boldyrev 2005, 2006): l 1/3 2/3 1/2 Measurements consistent with indices ranging from 1/2 to 3/4 17

18 Vor>city and Elsasser vor>city structures Can apply same methodology to vor>city structures and Elsasser vor>city structures by seung thresholds on or! =ẑ r v Sta>s>cs are nearly iden>cal as for current sheets!! ± =! ± j Elsasser vor>city structures can be understood by phenomenology (Zhdankin et al arxiv) 18

19 Dissipa>ve processes (flare events): 4D spa>otemporal objects consis>ng of points connected in space and in >me which exceed current density threshold In general, each process represents a set of structures interac>ng through mergers and divisions Iden>fica>on method: iden>fy spa>al structures in series of snapshots and track them across >me Zhdankin et al. PRL 2015, ApJ

20 Series of snapshots from simula>ons dumped at cadence (Δt) -1 Iden>fy all processes (using 4D threshold algorithm) and measure: Dura>on : >me from beginning of process to end of process Maximum spa>al scales: length, width, and thickness Peak energy dissipa>on rate: Z Dissipated energy: E = L max W max T max E max Z dt dv j 2 (integra>on across process) 20

21 Dura>on 0.5 Sta>s>cal asymmetry: more divisions than mergers 21

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23 Longest process Averaged evolu>on Average evolu>on is (t/ )E(t)dt t/ E = R nearly symmetric: 0 E(t)dt R 0 23

24 Dura>on Maximum length Dissipated energy α 1.75 Peak energy dissipa>on rate 24

25 T const. (dissipa>on scale) L max W max j j thr (iner>al range) (current densi>es near threshold) E max jthrl 2 max W max T max 2 E E max 3 25

26 Despite physical and methodological differences, sta>s>cs of dissipated energies and sizes are similar to solar flare observa>ons (e.g., Uritsky et al. 2007, Uritsky et al. 2013, Aschwanden et al. 2014) Sta>s>cs of dura>ons differ and solar flares are more asymmetric (e.g., Christe et al. 2008) More work needed to establish whether turbulence is responsible for similari>es, or is coincidental 26

27 Sta>s>cal analysis of dissipa>ve structures is a robust and informa>ve methodology for studying intermivency and magne>c reconnec>on in MHD turbulence Instantaneously, energy dissipa>on is evenly spread among current sheets spanning many iner>al-range scales and dissipa>on rates When the temporal dynamics are accounted for, energy dissipa>on is dominated by intense, large-scale dissipa>ve events (α 1.75) Dissipa>ve events have dura>ons propor>onal to maximum length Minor temporal asymmetry is observed, evidently due to energy cascade Promising comparison to solar flare sta>s>cs needs to be bever understood Connec>on between intermivent current sheets and magne>c reconnec>on in 3D turbulence remains unclear: X-points and current sheets do not necessarily coincide Zhdankin, V., Uzdensky, D.A., Perez, J.C. & Boldyrev, S. (2013) ApJ, 771, 124 Zhdankin, V., Boldyrev, S., Perez, J.C. & Tobias, S.M. (2014) ApJ, 795, 127 Zhdankin, V., Uzdensky, D.A., Boldyrev, S. (2015) PRL, 114, Zhdankin, V., Uzdensky, D.A., Boldyrev, S. (2015) ApJ, 881, 6 Zhdankin, V., Boldyrev, S. & Uzdensky, D.A. (2016) arxiv: (to appear in PoP) 27

28 PIC simula>ons reveal intermivency at kine>c scales (e.g., Wan et al. 2012, 2015; Leonardis et al. 2013, Karimabadi et al. 2013, TenBarge & Howes 2013) Decaying turbulence in PIC simula>ons of collisionless pair plasma are similar to MHD simula>ons at large scales (Makwana, VZ, et al. PoP 2015) MHD PIC Makwana et al

29 Current sheet size comparison Lengths Widths Thicknesses Iner>al-range scales are similar in both simula>ons Thickness scales with lauce in ideal MHD, but with ion skin depth in PIC