turbulence and intermittency in the solar wind r. bruno 1 in collaboration with: 3 carbone, v., 1...

Turbulence and Intermittency in the Solar Wind

R. Bruno1

In collaboration with: 3Carbone, V., 1Bavassano, B., 1D'Amicis, R., 4Sorriso, L., 5Pietropaolo, E

1 Istituto di Fisca dello Spazio Interplanetario, INAF, Rome, Italy3 Dipartimento di Fisica, Universita` della Calabria, Rende, Italy.4 Liquid Crystal Laboratory, INFM-CNR, Rende, Italy.5 Dipartimento di Fisica, Universita` di L'Aquila, Italy.

Turbulence and Multifractals in Geophysics and SpaceBelgian Institute for Space Aeronomy

Brussels, Belgium09-11 June 2010[background picture adapted from Chang et al., 2004]

typical IMF power spectrum in at 1 AU[Low frequency from Bruno et al., 1985, high freq. tail from Leamon et al, 1999]

Correlative Scale/Integral Scale: the largest separation distance over

which eddies are still correlated. Taylor scale:

The scale size at which viscous dissipation begins to affect the eddies.

it marks the transition from the inertial range to the dissipation range.

Kolmogorov scale: The scale size that characterizes the

smallest dissipation-scale eddies

Interplanetary fluctuations show a well developed turbulence spectrum

Turbulence and Multifractals in Geophysics and Space Brussels 9-11 June 2010

lC lT

2

T

Cmeff

R

(Batchelor, 1970)

typical IMF power spectrum in at 1 AU[Low frequency from Bruno et al., 1985, high freq. tail from Leamon et al, 1999]

Correlative Scale/Integral Scale: the largest separation distance over

which eddies are still correlated. Taylor scale:

The scale size at which viscous dissipation begins to affect the eddies.

it marks the transition from the inertial range to the dissipation range.

Kolmogorov scale: The scale size that characterizes the

smallest dissipation-scale eddies

Interplanetary fluctuations show a well developed turbulence spectrum


2

T

Cmeff

R

(Batchelor, 1970)

lC lT

Large scales: Origin of K-1 (flicker noise)

Matthaeus et al., ApJ, 2007

Observed in a wide variety of systems

first interpretation for the IMF due to Matthaeus and Goldstein, 1986:• within Alfvénic radius, merging of magnetic structures• multiplicative process and characteristic lengths

lognormally distributed• spectrum would derive from a superposition of several

similar samples recorded during long enough time interval

• It can be shown (Montroll and Shlesinger, 1982) that the spectrum S(f)~1/f

Ulysses


Compensated spectrum by Dmitruk et al., 2002-2004






Numerical modeling (Dmitruk et al., 2002-2004):• Upward traveling low frequency waves at coronal base

are capable of self-generating 1/f noise in density and B• 1/f not present in similar hydrodynamics simulations

(role of magnetic field)



Nakagawa and Levine, 1974






Numerical modeling (Dmitruk et al., 2002-2004):• Upward traveling low frequency waves at coronal base

are capable of self-generating 1/f noise in density and B • 1/f not present in similar hydrodynamics simulations

(role of magnetic field)

Full disk magnetograms (Nakagawa & Levine, 1974):• the1/k spectral region found in photospheric

observations seems to be a clear candidate for involvement in the appearance of the interplanetary 1/f signal.


Possible link between the structured surface of the sun and 1/f scaling in IMF

Telloni et al, ApJ, 706, 238, 2009

Proton density fluctuations* at 2.3 RSUN (UVCS/SOHO) are compared to Helios 2 measurements performed at 64 RSUN

Similar coronal imprint f-2 at large scales

Possible link also between the structured coronal base and in-situ observations of density fluctuations (Telloni et al., 2009)

(*) the fluctuations of Lyα emission observed in corona can be generally associated with neutral hydrogen density variations [Bemporad et al., 2008, Telloni et al., 2009] Turbulence and Multifractals in Geophysics

and Space Brussels 9-11 June 2010

• No intermittency at these scales• Fluctuations are already decorrelated (Gaussian) for time delays << stream

duration

Gaussianity of large scale fluctuations

Proton Gyrofrequencyfla

tnes

s

1 day

1 hour


102 103 104 105

0

30

60

90102 103 104 105

0

30

60

90

b^

v an

gle

time scale(sec)

F A S T W I N D 0.3 AU 0.7 AU 0.9 AU

b^

v an

gle

S L O W W I N D 0.3 AU 0.7 AU 0.9 AU

As the wind expands turbulence evolution and compressive effects decouple dB-dV in fast wind, starting from the largest scales

[see literature in Tu and Marsch 1995, Bruno and Carbone 2005]

Helios 2 observations

dB-dV alignment vs scale and heliocentric distance

ttBtV

tBtV

)()(

)()(cosˆ 1



Large scales are scarsely anisotropic

2

Power anisotropy at different scales

Intermediate scales characterized by turbulence scaling K-5/3



The presence of a Kolmogorov scaling implies that 0 zz

Since Z- cannot be of solar origin, the condition above requires generation mechanisms at work:

1) In the ecliptic, velocity shear (Coleman, 1968) and dynamic alignment (Dobrowolny et al., 1982, Matthaeus et al., 2008)

2) At high latitude, parametric decay is able to reproduce Ulysses observations (Bavassano et al, 2000, Malara et al, 2000)

102 103 104 105

0

30

60

90102 103 104 105

0

30

60

90

b^

v an

gle

time scale(sec)

F A S T W I N D 0.3 AU 0.7 AU 0.9 AU

b^

v an

gle

S L O W W I N D 0.3 AU 0.7 AU 0.9 AU

Intermediate scales are the most Alfvénic within fast wind

[see literature in Tu and Marsch 1995, Bruno and Carbone 2005]

Helios 2 observations

dB-dV alignment vs scale and heliocentric distance

ttBtV

tBtV

)()(

)()(cosˆ 1



small scales are strongly anisotropic,partly due to Alfvénic fluctuations

2

Power anisotropy at different scales

20 min


First anisotropy study in terms of k and k// in the solar wind by Bieber et al., 1996

Turbulence made of 2D+SLAB[Matthaeus et al., 1990]

Similar results by Horbury et al., 2008

K dominates on k// as we analyze directions at larger angles with magnetic field

Thus, the slab turbulence due to Alfvénic fluctuations would be a minor component of interplanetary MHD turbulence

Analysis performed in slow wind

Analysis performed in slow wind

2D

SLAB

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

2.000

25.50

49.00

72.50

96.00

119.5

143.0

166.5

190.0

C

R

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.000

6.500

12.00

17.50

23.00

28.50

34.00

39.50

45.00

C

R

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

max

min

min

max

min

max

2.000

7.375

12.75

18.13

23.50

28.88

34.25

39.63

45.00

C

R

0.9 AU

FAST WIND SLOW WIND

0.9 AU

MHD turbulence in terms of R and C (scale < 1hr)

1

2

22

RC

bv

bv

R

bvC

ee

ee

ee

bv

ee

ee

This difference affects the anisotropy

[adapted from Bruno et al., 2007]


Advected structures with magnetic energy excess

Alfvénic population

Bavassano et al., 1982 found that anisotropy of magnetic field fluctuations increases with heliocentric distance

[Bavassano et al., 1982]

Analysis performed with the same corotating stream observed at different heliodistances

321

12 /

13 /

anisotropy of magnetic field fluctuations increases with heliocentric distance

field compressibility increasese with heliocentric distance


It was shown that anisotropy is reduced by removing intermittent events from |B|, i.e. the most compressive magnetic events outside a normal distribution[Bruno et al., 1999]

[adapted from Bruno et al., 1999]

Local Intermittency Measure technique (Farge et al., 1990; Farge, 1992)

based on wavelet decomposition

)(),(22

,

4,2

FFw

wtLIM

tt

ttt

The Flatness Factor of the wavelet coefficients at a given scale , i.e.

LIM2 , is equivalent to the Flatness Factor FF of data at the same scale (Meneveau, 1991 )

Thus, values of FF()>3 allow to localize events which lie outside the Gaussian statistics and cause Intermittency.

Proton Gyrofrequency

Intermittency at these scales doesn’t seem to be due to dissipative processes

Inertial range

Anomalous scaling of IMF is well inside inertial range

Proton Gyrofrequency

Intermittency starts within the inertial range at about 2 decades away from the dissipation range.

flatn

ess

20

PDFs of other parameters can be rescaled

The PDF of , dr dB2, drV2, dVB2 can be rescaled under the following change of variable

),(),( xPxP s(Hnat et al., 2002, 2003, 2004)

The height of the peaks rescales

This study showed that:• the distribution is non Gaussian but it is stable and symmetric and can be described by a single parameter monofractal

•The process can be described by a finite range Lévy walk (scales up to 26 hours)•A Fokker-Planck approach can be used to study the dynamics of PDF(db2)


Local Intermittency Measure technique allows to locate intermittent events(Farge, 1990)

56000 60000 64000 68000 72000

260

280

300

320

340

360

380

spee

d &

res

idua

ls [

km/s

ec]

day 22.02.2001[sec]

Cluster s/c 3 data

(Bruno and Carbone, 2005)

The waiting times are distributed according to a power law PDF(Δt) ~ Δt-β long range correlations

Thus, the generating process is not Poissonian.



56000 60000 64000 68000 72000

260

280

300

320

340

360

380

spee

d &

res

idua

ls [

km/s

ec]

day 22.02.2001[sec]

Cluster s/c 3 data

180 190 200 210 220

-290

-280

-270

-260

-250

-240

-230

Maximum variance plane

Max

Var

MedVar

this intermittent event marks the border between different plasma regions



56000 60000 64000 68000 72000

260

280

300

320

340

360

380

spee

d &

res

idua

ls [

km/s

ec]

day 22.02.2001[sec]

Cluster s/c 3 data

ByBx

Bz

VyVx

Vz

Two different regions are identified and fluctuations within each of them are Alfvénic

Magnetic field in Alfvén units


Several studies on events similar to the previous one contributed to formulate the spaghetti-like model [Bruno et al., 2001]

A spacecraft crossing this structure would record a series of intermittent events embedded in an ocean of Gaussian, Alfvénic fluctuationss/c trajectory

the sharp directional changes of magnetic field occurring typically across interwoven flux tubes can lead to slow magnetic reconnection and additional heating of the solar wind.[Vörös et al., 2010]

[Tu and Marsch, 1992]

[Bieber, Wanner and Matthaeus, 1996]

2D+SLAB

(Chang et al., 2002)

Similar pictures

2D+SLAB

Several contribution have been given in this direction in the past years (Thieme et al., 1988, 1989; Tu et al., 1989, 1997; Tu and Marsch, 1990, 1993; Bieber and Matthaeus, 1996; Crooker et al., 1996; Bruno et al., 2001, 2003, 2004; Chang and Wu, 2002; Chang, 2003; Chang et al., 2004; Tu and Marsch, 1992, Chang et al., 2002, Borovsky, 2006, 2009, Li, 2007, 2008, Vörös et al., 2010)

Structures producing intermittency might be either of solar nature and advected by the wind or locally generated by non-linear turbulence evolution

Some remarks

Compressive events increase intermittency

Intermittent events can increase the power anisotropy of fluctuations

Then: compressive events might play a role in power anisotropy


With this in mind, we look at power anisotropy beyond fC

[Leamon et al., 1998, 1999, Bale et al.,

2005, Hamilton et al., 2008, Podesta,

2009, Sahraoui et al., 2009, etc…]

Some remarks

Compressive events increase intermittency

Intermittent events can increase the power anisotropy of fluctuations

Then: compressive events might play a role in power anisotropy


Power anisotropy study from Podesta, 2009

[cur

ves

arbi

trar

ily s

hift

ed v

ertic

ally

]

[ q angle between local mean field and radial direction]

KAWs cascade

KAWs dissipation??

Inertial range: • energy cascade directed primarily perpendicular to the mean

mag field [Shebalin et al., 1983; Oughton et al., 1994; Matthaeus et al., 1996]• power anisotropy increaseses with wavenumber

“Dissipation” range: • The new cascade (KAWs?) starts at ki 1 [i.e. S/C 0.5Hz, in

this case] when the fkuid-like behavior breaks down• power anisotropy increaseses with wavenumber• The second peak marks beginning of KAWs dissipation?

FFT

wavelets

Observational evidence for Alfvén waves – KAWs transition in the solar wind [Bale et al., 2005, Cluster data]

Moreover, Sahraoui et al., 2009 extended the study to the electron gyroscale where they identified dissipative processes of KAWs

electric field and magnetic field k−5/3

inertial sub-range is observed up to ki~1 (Electric spectrum arbitrarily offset to overlap magnetic spectrum)

the wave phase speed in this regime is shown to be consistent with the Alfvén speed

The red curve approximates the dispersion relation for KAWs (vk2i

2). For whistler waves (vki). it would run much lower for ki>1 [Bale et al., 2005]

Good correlation between the electric and magnetic power (as black dots) and good cross-coherence of Ey with Bz (as bluedots) suggest KAW

eciAei

ecithei

ei

ei

V

V

,,

,,

/

/

,

,

29

(Alexandrova et al., 2008, 2009)

The presence of a power-law spectrum (instead of a rough exponential cutoff) and the increase of intermittency suggest the presence of a new cascading range (Stawicki et al., 2001, Bale et al., 2005, Sahraoui et al., 2006, 2009)

The cascade has a compressible character. Compressibility seems to govern the spectral index k-7/3+2a where a is the compressibility (Alexandrova et al., 2008, 2009)

A new cascading range beyond fci confirmed by by Alexandrova et al., 2008, 2009 using Cluster magnetic observations

Inte

rmitt

ency

incr

ease

s



Hollweg, 1999:• KAWs become strongly compressive when ki 1. • The compression is accompanied by a magnetic field fluctuation δB ‖ such that the total pressure perturbation δp tot ≈ 0

Inte

rmitt

ency

incr

ease

s


A new cascading range beyond fci confirmed by by Alexandrova et al., 2008, 2009 using Cluster magnetic observations


Different conclusions about intermittency in the “dissipation” range

[Kiyani et al., PRL 2009]

monofractal

multifractal

Time series and probability distribution function for the max eigenvalue at three different scales (46s, 1.5s, 0.2s)

(Perri et al., 2009)(Perri et al., 2009)

Perri et al., 2008, 2009, performed a minimum variance study in this frequency range, focusing on the anisotropy of the fluctuations

• The PDFs evolve with the scale, becoming power laws at scales smaller than the ion cyclotron scale.

• Similar behaviour for the other eigenvalues

What is the possible mechanism to reproduce this behavior?

Cluster mag data resolution f=22Hz

Intermittent behavior

Power law

Looking at the distribution of angular fluctuations of B vector on a time scale of 0.045 sec (i.e.22Hz)

~6 minutes


~6 minutes

Looking at the distribution of angular fluctuations of B vector on a time scale of 0.045 sec (i.e.22Hz)

Distribution obtained from Cluster 1,2,3,4 data at the time scale of 0.045s


Same type of distribution at larger scales, within the inertial range


[°] a

Alfvénic turbulence Coherent

structures

(Bruno et al., 2004)

Distribution obtained from Helios data at the time scale of 6s, high frequency termination of the inertial range

whistlers and KAW ?


A Toy Model to reproduce Cluster observations

a

We allow the tip of a vector to move randomly on the surface of a sphere. The distribution of

the angle a between 2 successive orientations of the vector follows the double-lognormal distribution obtained from Cluster observations



Compressions added: s|B|/<|B|>~3%

• moreover, we added compressions in the field intensity• we tried to reproduce the same compressive level found in real data (similar spectra)• compressions revealed to play an important role in this toy model (see next slides)

Compressibility(f) S|B|(f)/SC(f)


Time series and probability distribution function for the max eigenvalue at three different scales (46s, 1.5s, 0.2s)

(Perri et al., 2009)(Perri et al., 2009)

minimum variance study by Perri et al., 2008, 2009

• The PDFs evolve with the scale, becoming power laws at scales smaller than the ion cyclotron scale.

• Similar behaviour for the other eigenvalues

Cluster mag data resolution f=22Hz

Intermittent behavior

Power law


10000 15000 20000 250000.00

0.05

0.10

0.1510000 15000 20000 25000

0.0

0.1

0.2

10000 15000 20000 250000.0

0.2

0.4

0.6

time in arbitrary units

1

scale: 5 pts

1

scale: 38 pts

1

scale: 1150 pts

0.1 1101

102

103

104

0.01 0.1100

101

102

103

104

0.01 0.1100

101

102

103

104

PD

F( 1)

scale 1150

PD

F( 1)

scale 38

PD

F( 1)

1

scale 5

The Toy Model reproduces qualitatively the results obtained in the solar wind

(from Toy-Model)(from Toy-Model)

Max eigenvalue behavior from Toy Model


10000 15000 20000 250000.00

0.05

0.10

0.1510000 15000 20000 25000

0.0

0.1

0.2

10000 15000 20000 250000.0

0.2

0.4

0.6


1

scale: 5 pts

1

scale: 38 pts

1

scale: 1150 pts

0.1 1101

102

103

104

0.01 0.1100

101

102

103

104

0.01 0.1100

101

102

103

104

PD

F( 1)

scale 1150

PD

F( 1)

scale 38

PD

F( 1)

1

scale 5

(from Toy-Model)(from Toy-Model)

Max eigenvalue behavior from Toy Model

intermittent character

Gau

ssia

n ch

arac

ter

-15 -10 -5 0 5 10 15

1E-4

1E-3

0.01

0.1

1

PD

F

1 /

compression~6% scale 5 scale 1150


15500 16000 16500 170000

20

40

60

80

14000 16000 18000 200000

20

40

16400 16500 16600 16700 16800 169000

20

40

60

80

scale 38 pts

scale 1150 pts


scale 5 pts

(from Perri et al., 2009) (from Toy-Model)

Time behavior of the angle Q between minvar direction and mean field direction at three different scales.

Similar profiles obtained from toy model

Results from Cluster


(from Perri et al., 2009)

Striking similarity between these PDFs and those found in the SW

PDFs in the Solar Wind

Dt=46 secDt=1.5 secDt=0.2 sec

(from Toy-Model)



The effect of compressions


With compressions

W/O compressions

Without compressions the toy doesn’t work wellTurbulence and Multifractals in Geophysics

and Space Brussels 9-11 June 2010


summary

• k-1 frequency range: possible link with the structured surface of the sunfluctuations are Gaussianpower anisotropy (P/P// >1) increaseses with wavenumber

• k-5/3 inertial range: fluctuations mixed with advected structuresintermittency more than 2 freq. decades before the “dissipation range”, intermittency linked to compressive structures and current sheets. possible flux tube structurepower anisotropy (P/P// >1) increaseses with wavenumber

• Beyond the proton cyclotron freq.: new cascade (KAWs or/and whistlers) intermittency increases again, important role played by compressions confirmed by anisotropy studies

(Feng et al., 2007)

These flux tubes should look like interplanetary flux ropes

Force-free structure for which

BJB

(Lundquist, 1950)

WIND data, 20-09-1995

Some helicity mesure should be able to unravel the presence of these structures

Measurements in the solar wind, onboard a spacecraft, are essentially collinear along the radial direction, so a full Fourier decomposition is not possible and we have to reduce to one-dimensional spectra (reduced spectra)

Matthaeus and Goldstein (1982) provided the following expression for the reduced spectrum of Hm

11231 Im2 )/k(kS)(kH rrm

48

In practice, if collinear measurements are made along the X direction, the reduced magnetic helicity spectrum is given by:

1

1

Im2

k

ZY)(kH

*rm

where Y and Z are the Fourier transforms of By and Bz components, respectively

The tensor S23 is the Fourier transform of the correlation function R23

Results in the solar wind do not show a definite sign

Within the MHD regime, Hm has no clear dominant sign in the inertial range, especially at high frequencies

(Goldstein et al., 1991)(Matthaeus and Goldstein, 1982)

)(

)()(

kE

kHkk

b

mm

Adopting the wavelet transform to study Hm in the solar wind

k

(k)](k)B[B

k

(k)][S(k)H z

*y

rrm

Im2Im2 23 k

(k,t)](k,t)W[W(k,t)H zyr

m

*Im2

(k,t)E

(k,t)k H(k,t)σ

r

rm

m

a wavelet is a localized function which can be translated and re-scaled

τ

t'tψ

τ(t)ψt',τ

1

unlike the Fourier transform, the wavelet transform allows to unfold a signal both in time and frequency (or space and scale). Wavelet analysis is particularly useful to study non-stationary processes

Wy(k,t) and Wz(k,t) wavelet transform of By(t) and Bz(t)

Normalized magnetic helicity

Handed-Left 0σ

Handed-Right 0σ

m

m

)(

)(

k

k

re

re

The normalized magnetic helicity (sm) helps to easily estimate

the "handedness“ of magnetic field fluctuations

)()(

)()(

)(

)()(

kEkE

kEkE

kE

kHkk

RL

RL

b

mm

sm

Helios 2

Wavelet analysis on magnetic helicity within 1 day of slow wind at 0.3 AU

BY

B Z

BY

B Z

rectangles indicate limits in scale and time

negative helicity(right-handed)

mixed helicity

sm

Wavelet analysis on magnetic helicity within 1 day of slow wind at 0.3 AU

from 11.6 to 12.8

from 12.8 to 14.2

(negative helicity, right-handed)

sm

Flux rope spotted by Feng et al., 2007

Wavelet analysis on magnetic helicity within 1 day of WIND data containing a flux-rope

Band pass filtered between 15 min and 2 hrs

WIND data, 20-09-1995

Preliminary magnetic helicity analysis shows some similarities during ACE and ULYSSES alignment in 2007

1AU 1.4AU

Sca

le[h

r]

Sca

le[h

r]

Some of the helicity structures seen by ACE at certain scales reach Ulysses, 0.4 AU away in spite of the fact that the stream has strong velocity gradients in itMore quantitative analysis is needed.

1

2

3

4

5

1

2

3

4

5

Coherent, helical structures observed in the solar wind recall magnetic field lines trapped in filamentary structures dominated by 2D turbulence as in the model by Ruffolo et al., 2003, and Chuychai et al., 2007

(Ruf

folo

et a

l., 2

003,

Chu

ycha

i et a

l., 2

007)

2D dominated

slab dominated

In the 2D turbulence field lines follow contours of constant “a” remaining trapped near some (x,y) point

Some similarity is found between IMF coherent structures and Ruffolo et al (2003) and Chuychai et al. (2007) model

(Bruno et al., in preparation)

Recent 2.5D compressible MHD simulations (Servidio et al., 2008) also showed the formation of islands of well defined magnetic helicity

sm

(Servidio et al., 2008)

sm

mean field

local field

• In the presence of a mean field along z the islands are the footprints of elongated flux-tubes

• Current sheets are formed locally between the islands

(Servidio et al., 2008)

(Ruffolo et al., 2003)

(Chuychai et al., 2007)

Filamentary structures, connected to the sun, would cause the observed (Mazur et al.,

2000) SEP “dropouts” from impulsive solar flares (Ruffolo et al., 2003, Chuychai et al., 2007)

Energy range: 20keV/nucleon to 2MeV/nucleon

wavelet analysis might help to prove this hypothesis identifying flux tubes

(Bruno et al., in preparation)

Cluster Toy Model

distribution vs compressibility at different scales


0 20 40 60 80

0.0

5.0x102

1.0x103

1.5x103

(from Toy-Model)

PD

F

between minvar and <B>

|B|

/<|B|>~60%window:

1150 38 5

PDFs in the magnetosheath

It is sufficient to increase the compressive level to obtain distributions similar to those recorded in the magnetosheath




extracted from Gaussian distribution

extracted from uniform distribution

Also the type of DQ distribution plays a role, the same level of compression is not longer sufficient


Anomalous jumps of the field vector identified as source of intermittency (Bruno et al., 2001, 2004, Borovsky, 2008, Li, 2008)

6 3 0-3-6

-6-3036

-6-3036

6 3 0-3-6

-6-3036

-6-3036

6 3 0-3-6

-6-3036

-6-3036

6 3 0-3-6

-6-3036

-6-3036

CB

from: 49.612to: 49.646

Helios 2, 6s avgs

E

D

from: 49.654to: 49.690

D C

from: 49.628to: 49.674

BA

from: 49.598to: 49.623

Time sequence 2hr 13 min

6 4 2 0 -2 -4 -6 -8

-8

-6

-4

-2

0

2

4

6

-8-6

-4-2

0246

Helios 2, 6sec, 49.628-49.674 (~66min)

Bz

By

Bx

these directional jumps are generally associated to discontinuities in field magnitude and/or density (Bruno et al., 2001)

Directional fluctuations follow a double log-normal

[°] a

Alfvénic turbulence Coherent

structuresFlux tubes

[Bruno et al., 2004]

Similar results found by Borovsky (2008)

Alfvénic turbulence

Coherent structuresFlux tubes

Largest jumps due to convected structures like discontinuities

Directional fluctuations follow a double log-normal

These results corroborated by a recent analysis by Li (2008) who studied the behavior of the cumulative probability of having large . Li identified 2 populations: turbulent fluctuations and current-sheet-like structures

[Bruno et al., 2004]

a

We allow the tip of a vector to move randomly on the surface of a sphere. The distribution of

the angle a between 2 successive orientations of the vector follows a double-lognormal distribution


Distribution of magnetic field intensity fluctuations at the smallest scale directly taken from real Cluster S/C1 data

A Toy Model to reproduce Cluster observations

0.1100

101

102

103

0.1

101

102

103

0.1

101

102

103

0.1 1100

101

102

103

0.1 1100

101

102

103

0.1 1100

101

102

103

PD

F(

3/ 1)

scale 1150

PD

F(

3/ 1)

3/

1

scale 5

PD

F(

3/ 1)

scale 38

PD

F(

2/ 1)

scale 1150

PD

F(

2/ 1)

2/

1

scale 5

PD

F(

2/ 1)

scale 38

Ratio of the eigenvalues(from Perri et al., 2009) (from Toy-Model)

The Toy-Model reproduces the behaviour of the ratio of the eigenvalues. As already noticed by Perri et al., 2009, at smaller scales values of l2/l1<0.1 have a large probability to occur so that fluctuations are quasi-one-dimensional.


Interplanetary fluctuations show self-similarity properties

30 days

16 hours

72 minutes

)μ(r)v(r)v(

The solution of this relation is a power law:

hC )v(


turbulence and intermittency in the solar wind r. bruno 1 in collaboration with: 3 carbone, v., 1...

Documents

scale size

taylor scale

kolmogorov scale

dissipation range

space brussels

viscous dissipation

spectrum sf

typical imf power spectrum