Z. V örös University of Innsbruck, Austria Acknowledgements:

Brussels-2010 Vörös: Turbulence in the magnetotail, University of Innsbruck, Austria

Z. Vörös University of Innsbruck, Austria

Acknowledgements: A. 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)

Turbulence and intermittencyin the Earth‘s magnetotail FWF

ProjectSupport


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 RECONNECTIONARE USUALLY NOT INDEPENDENT;


MOTIVATION - OUTLINE

• Turbulence, magnetic reconnection, system-wide dynamical responses in the Earth´s magnetosphere;


Turbulence in the magnetosphere

Numbers estimated by Borovsky et al., 1997 andBorovsky & Funsten, 2003; supposing e.g. for Rethat the kinematic viscosity can be obtained from Coulomb collisions

Re=VL / ~ 1011

Rm=VL/ ~ 1013

Re=VL / Rm=VL/

L

V

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/ LThe smallest scale S in a cascade: S ~ (3/ <>)1/4 L / S ~ (Re)3/4

Fully developed turbulence: Re~> 104


Scaling and SOC in the magnetosphere

Hasegawa et al. Nature, 2004

TURBULENCE & SELF-ORGANIZATION IN THE MAGNETOSPHERE

Shock assoc. Cusp Magnetosheath K-H boundary layer

Plasma sheet

BorovskyChaos & 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.)


Turbulent spectra: geospaceDownstream of the bow shockAlexandrova et al., 2004

MagnetosheathDownstream of QP bow shockYordanova et al., 2008

Cusp regionNykyri et al. 2006

Plasma sheetVolwerk et al., 2004

slope:3.5

slope:2.4

slope:1.66

slope:4.9

slope:2.5-2.7


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


Turbulence in the plasma sheet Walker et al., Space Sci.Rev., 1999

e.g. Kivelson & Russel, Intro to Space Physics,1995

~ 3

0-5

0 R

E

e.g. Hughes, 1995; in K&R

BurstyFlow1-3RE


Turbulence in the plasma sheetBursty 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 theion 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


BBF associated turbulence

Scaling region,scaling index,Reynolds number,

all depend onthe <bulk speed>.

Doppler shift +spectral widening

spectralwidening


Stationarity vs. intermittencyPlasma 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


Individual vs. multiple flows

Individual flows: stationary Multiple flows: mixed, non-stationary

Independentdriving sources

Vörös et al. 2006


Check of Taylor hyp. : temporal vs. spatial

TWO-POINTSpatial fluctuationsbetween Cluster 1,4:

ONE-POINTTime-delayed fluctuations:

(Vörös et al. 2006)


Multifractals: multinomial measures


A recursive construction rule


LIM: Local Intermittency Measure

f()

The strength of localburstiness (Hölder exponent)

(See also Bruno et al., 1999, Consolini & DeMichelis, 2005)



LIM analysis in the magnetotail



LIM: cross-scale coupling + dipolarization



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).


Nonlocal interactions and intermittency


Possible flowgeometry

3700 km



4

3

2

1

1

2

3

4

Skewness and Kurtosis

Scale [s]


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.


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


Reconnection+BBF+ turbulence

Sweet-Parker, 1957 Petschek, 1964 Hall, two-fluid, eg. Oireoset et al., 2001

Fast but unstableand not observed

SlowTurbulent in 3DLazarian & Vishniac, 1999

Fast

Fast

FAST: 1.) collisionless regime 2.) Hall-signatures; 3.) thin current sheet (large-scale reorganization of B) 4.) turbulent B?

CLUSTER

THEMIS

AB

C4C1

C3

C2

C

Hoshino et al. 2001

Runov et al., 2003

Nagai et al., 2001

Baumjohann & Nakamura, 2006

B V

Bx

BY

Quadrupolar Hall magnetic field

Bx

By

X

Z

CLUSTER MEASUREMENTS


Large-scale topological changes preceeding reconnection

dipolarization

Sudden changesin B directionat the positionsof Clusterand Goes

Laitinen et al., 2007


Large-scale topological changes preceeding reconnection

Sudden changesin B directionat the positionsof Clusterand Goes

Directional changes of the ambient magnetic field at Cluster

Laitinen et al., 2007


THEMIS resultsAngelopoulos et al., 2008

Large-scale reconnection signatures

Angelopoulos et al., 2008

Earthward flows+vortices

heating

Flow reversal

Dipolarization

Strong interaction + flapping

Does the increase of density stop the reconnection??

Vörös et al., 2009


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 themagnetosphere: substorms;• Substorms lead to large-scale reorganizations of B.


Second-order non-stationarity

Earth‘smagnetosphere

Solarwind

Q – goodness of fit measureQ>>0.05 is OK

single flow

multiple flows Vörös et al. 2010

1 day2 months

Z. V örös University of Innsbruck, Austria Acknowledgements:

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