WAVES AND TURBULENCE IN
SOLAR-TERRESTRIAL PLASMAS
Turbulence in the Solar Wind: an Overview
1Roberto
Bruno
In collaboration with:
1Bavassano, B., 1D'Amicis, R.,
2Carbone, V., 3Sorriso-Valvo, L.
1) Istituto Fisca Spazio Interplanetario-INAF, Rome, Italy.
2) Dpt. Fisica, Universita` della Calabria, Rende, Italy.
3) Liquid Crystal Laboratory, INFM-CNR, Rende, Italy.
RAS Lecture Theatre, Burlington House,
Piccadilly, London, 12 March 2010
30 days
Interplanetary fluctuations show
self-similarity properties
v( )  μ(r)v(r )
16 hours
The solution of this relation is a power law:
v(  )  Ch
72 minutes
RAS Lecture Theatre, Burlington House,
Piccadilly, London, 12 March 2010
The first evidence of the
existence of a power law in
solar wind fluctuations
First magnetic energy spectrum
(Coleman, 1968)
RAS Lecture Theatre, Burlington House,
Piccadilly, London, 12 March 2010
10
5
10
4
10
3
10
2
10
1
10
0
10
-1
10
-2
10
-3
10
-4
10
k-1
k-5/3
Energy
containing
scales
-7
10
-6
-5
1x10 1x10
-4
Inertial
range
10
-3
-2
10
 the largest separation distance over
which eddies are still correlated. i.e.
the largest turb. eddy size.
 Taylor scale:
 The scale size at which viscous
dissipation begins to affect the eddies.
 Several times larger than Kolmogorov
scale
 it marks the transition from the inertial
range to the dissipation range.
Diss.
range
fc
10
 Correlative Scale/Integral Scale:
Kolmogorov scale
10
6
Taylor scale
7
Correlative scale
10
2
power density [ /Hz]
Characteristic scales in turbulence spectrum
-1
10
0
frequency [Hz]
10
1
 Kolmogorov scale:
 The scale size that characterizes the
typical IMF power spectrum in at 1 AU
smallest dissipation-scale eddies
[Low frequency from Bruno et al., 1985, high freq. tail from Leamon et al, 1999]
 C
Rm  
T

RAS Lecture Theatre, Burlington House,
Piccadilly, London, 12 March 2010



2
(Batchelor, 1970)
The Taylor Scale and Correlative Scale can be obtained from the two
point correlation function
R(r )  V ( x  r )V ( x)  x /  (V ( x))2 
• Taylor scale:
– Radius of curvature of the
Correlation function at the
origin.
– Scale at which turbulent
fluctuation are no longer
correlated.
Correlation function R(r)
• Correlative/Integral scale:
Main features of the
correlation function R(r)
f (0)  1
f (0)  0
f (0)  1 / T2
f ( )  0
(adapted from Weygand et al., 2007)
RAS Lecture Theatre, Burlington House,
Piccadilly, London, 12 March 2010
We can determine:
• the Taylor Scale from Taylor expansion of the two point correlation
function for r0:
r2
Rr   1 

2
2T
(Tennekes, and Lumley , 1972)
where r is the spacecraft separation and R(r) is the auto-correlation function.
• the Correlative Scale from:
Rr   R0 exp  r / C 
(Batchelor, 1970)
• the magnetic Reynolds number from:
 C
Rm  
 T



2
(Batchelor, 1970)
•First experimental estimate of the Reynold’s number in the solar wind (previous
estimates obtained only from single spacecraft observations using theTaylor
hypothesis)
•First evaluation the two-point correlation functions using simultaneous
measurements from Wind, ACE, Geotail, IMP8 and Cluster spacecraft (Matthaeus
et al., 2005).
Cluster in the SW
Geotail+IMP 8
ACE+Wind
Separations (km)
(Matthaeus et al., 2005, Weygand et al., 2007)
RAS Lecture Theatre, Burlington House,
Piccadilly, London, 12 March 2010
Experimental evaluation of C and T in the solar wind at 1 AU
Cluster
Wind & ACE
Cluster
(parabolic fit)
(exponential fit)
T 
km
C  1.3∙106 km
2.4∙103
eff
m
R
 C
 
 T
2

  2.3 105

(Matthaeus et al., 2005
Weygand et al., 2007)
high Reynolds number  turbulent fluid  non-linear interactions expected
The shift of the spectral break suggests the presence of non-linear
interactions
(Tu , 1984)
•Non-linear interaction are responsible for this evolution
•More developed turbulence implies larger Re and larger inertial range
Alfvénic correlations in the solar wind
0.3 AU
Slow wind:
fluctuations
scarcely Alfvénic
Fast wind:
fluctuations
strongly Alfvénic
b^v angle
90
B-V alignment
Alfvénicity and radial evolution
60
SLOW WIND
0.3 AU
0.7 AU
0.9 AU
30
0
2
b^v angle
90
60
10
3
10
4
10
3
10
4
10
10
5
FAST WIND
0.3 AU
0.7 AU
0.9 AU
different scales and
different heliocentric
distances for SLOW and
FAST wind
30
0
2
10
10
5
time scale(sec)
Helios 2 observations
11
The shift of the spectral break suggests the presence of non-linear
interactions
(Tu , 1984)
•Non-linear interaction are responsible for this evolution
•More developed turbulence implies larger Re and larger inertial range
Spectral breakpoint within high latitude solar wind
In the polar wind the
breakpoint is at smaller scale
than at similar distances in the
ecliptic wind.
Thus, spectral evolution in the
polar wind is slower than in
the ecliptic wind.
Horbury et al., Astron. Astrophys., 316, 333, 1996
13
To develop non-linear interactions we need to have the
simultaneous presence of both Alfvén modes Z+ and Z

z   
1 
B2 
2
 n z
 (z  )z    p 
t
 
8 
    
z  u  b  u  B / 4
Incompressible Navier-Stokes equation for the
MHD case
Rv ,m 
z±  velocity field
P  total pressure
n  kinematic viscosity
 
u  0
non  linear
 105  106
dissipativ e
Nonlinear interactions and the consequent energy
cascade need both Z+ and Z14
Fast Wind
1.
2.
3.
Z+ are the majority modes
Turbulence spectra evolve within fast wind
Spectral index towards -5/3
0.3 AU
definition
e±(k)=FT[z±(t)]
0.9 AU
e+
f –1
e+
f –5/3
e–
e–
Marsch and Tu, JGR, 95, 8211, 1990
For increasing distance
the e+ and e– spectra
approach each other
(e+ decreases faster
than e– )
At the same time the
spectral slopes evolve,
with the development
of an extended f –5/3
regime.
Slow Wind
1.
2.
3.
Quasi equipartition between Z+ and Z- modes
Turbulence is frozen, does not evolve
Spectral index remains at -5/3 (Kolmogorov)
0.9 AU
0.3 AU
No much radial evolution
e+
f –5/3
e–
e+
f –5/3
e–
Turbulence development reflected in the radial
evolution of sC in the ecliptic
Normalized cross-helicity
e  e
sc   
e e
Helios 1*
Voyager*
Radial depletion of sc
implies local generation
of e- modes
[Adopted from Matthaeus et al., 2004]
*mixing fast and slow wind
sC  0
Different origin for Z+ and Z- modes in interplanetary space
20 RS
Z+
Z+
Alfvén radius
ZZOutside the
Alfvén radius we
need Z- modes in
order to have

Z+



Z   Z   0
Need for a
mechanism able
to generate Zmodes locally
RAS Lecture Theatre, Burlington House,
Piccadilly, London, 12 March 2010
Z+
Turbulence development reflected in the radial
evolution of sC in the ecliptic
Normalized cross-helicity
e  e
sc   
e e
Helios 1*
Voyager*
Radial depletion of sc
implies local generation
of e- modes
[Adopted from Matthaeus et al., 2004]
*mixing fast and slow wind
sC  0
Turbulence development reflected in the radial
evolution of sC in the ecliptic
e  e
sc   
e e
Helios 1*
Voyager*
To fit the radial
behavior of sC
Matthaeus et al (2004)
proposed a mechanism
based on Velocity
shear and dynamic
alignment
[Adopted from Matthaeus et al., 2004]
20
*mixing fast and slow wind
velocity shear :
(Coleman, 1968)
Quickly generates Z- modes contributing to decrease the alignment
between B and V  |sC| decreases
dynamic alignment
(Dobrowolny et al., 1980)
Same energy transfer rate for dZ+ and dZ- along the spectrum,
towards dissipation. An initial umbalance dZ+ >> dZ- would end up in
the disappearance of the minority modes dZ-  |sC| increases
RAS Lecture Theatre, Burlington House,
Piccadilly, London, 12 March 2010
Turbulence generation in the ecliptic: velocity shear mechanism
(Coleman 1968)
• Solar wind turbulence may be locally
generated by non-linear processes
at velocity-shear layers.
• Magnetic field reversals speed up
the spectral evolution.
This process might have a relevant
role in driving turbulence evolution
in low-latitude solar wind, where a
fast-slow stream structure and
reversals of magnetic polarity are
common features.
The z+
spectrum
evolves
slowly
The 6 lowest
Fourier modes of B
and V define the
shear profile
Alfvén
modes
added
T=3 ~ 1 AU
A z– spectrum is
quickly
developed at
high k
2D Incompressible simulations by Roberts et al., Phys.
Rev. Lett., 67, 3741, 1991
22
Typical velocity shear region
Turbulence generation in the ecliptic: velocity shear mechanism
(Coleman 1968)
• Solar wind turbulence may be locally
generated by non-linear processes
at velocity-shear layers.
• Magnetic field reversals speed up
the spectral evolution.
This process might have a relevant
role in driving turbulence evolution
in low-latitude solar wind, where a
fast-slow stream structure and
reversals of magnetic polarity are
common features.
The z+
spectrum
evolves
slowly
The 6 lowest
Fourier modes of B
and V define the
shear profile
Alfvén
modes
added
T=3 ~ 1 AU
A z– spectrum is
quickly
developed at
high k
2D Incompressible simulations by Roberts et al., Phys.
Rev. Lett., 67, 3741, 1991
24
velocity shear :
(Coleman, 1968)
Quickly generates Z- modes contributing to decrease the alignment
between B and V  |sC| decreases
dynamic alignment
(Dobrowolny et al., 1980)
Same energy transfer rate for dZ+ and dZ- along the spectrum,
towards dissipation. An initial umbalance dZ+ >> dZ- would end up in
the disappearance of the minority modes dZ-  |sC| increases
RAS Lecture Theatre, Burlington House,
Piccadilly, London, 12 March 2010
Dynamic alignment
(Dobrowolny et al., 1980)
This model was stimulated by apparently contradictory observations
recorded close to the sun by Helios:
1. observation of sC  1 means correlations of only one
type (Z+)
absence of non-linear
interactions
2. turbulent spectrum clearly observed
presence of non-linear
interactions
?
26
Alfvénic correlations in the solar wind
0.3 AU
Fast wind
fluctuations
strongly Alfvénic
Outward modes
largely dominate
Dynamic alignment
(Dobrowolny et al., 1980)
ti ~

Interactions between Alfvénic fluctuations are local
in k-space
We can define 2 different time-scales for these
interactions
The Alfvén effect increases
the non-linear interaction
time
We can define an
energy transfer rate
ta ~


t
C A

 i
T ~ t i

tA
(Z  )2
  ~
(Z  )2
T 

Z 

Ca
~ - 1C A1 (Z  )2 (Z  )2
The energy transfer rate is the same for dZ+ and dZAn initial unbalance between dZ+ and dZ- , as observed close to the Sun, would
end up in the disappearance of the minority modes dZ- towards a total
alignment between dB and dV as the wind expands
28
However, velocity shear and dynamic alignment do not explain
the radial behavior of the normalized residual energy sR
e e
sR  v b
e e
v
b
Magnetic energy eb
dominates on kinetic
energy ev during the wind
expansion
Adapted from Roberts et al., JGR, 95, 4203, 1990
29
The following analysis will focus on this problem since
the presence of magnetically dominated fluctuations
suggests the presence of advected structures
i.e.
low frequency solar wind fluctuations are not only due
to turbulent evolution of Alfvénic modes
1.0
max
0.8
190.0
0.3 AU
0.6
166.5
0.4
143.0
0.2
119.5
96.00
0.0
sR
Radial evolution of MHD turbulence
in terms of sR and sC (scale of 1hr)
72.50
-0.2
49.00
-0.4
25.50
min
-0.6
2.000
-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
sC
1.0
max
0.8
45.00
0.6
39.50
0.4
34.00
0.2
28.50
23.00
sR
0.0
17.50
Alfvénic population
e  e 2  v  b 
sC     v b
e e
e e
ev  eb
sR  v b
e e
s C2  s R2  1
-0.2
12.00
-0.4
6.500
min
-0.6
1.000
-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
sC
1.0
max
0.8
45.00
0.6
39.63
0.4
34.25
0.2
28.88
23.50
sR
0.0
18.13
-0.2
12.75
-0.4
7.375
min
-0.6
2.000
-0.8
-1.0
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
sC
0.2
0.4
0.6
0.8
1.0
31
1.0
max
0.8
190.0
0.3 AU
0.6
166.5
0.4
143.0
0.2
119.5
96.00
0.0
sR
Radial evolution of MHD turbulence
in terms of sR and sC (scale of 1hr)
72.50
-0.2
49.00
-0.4
25.50
min
-0.6
2.000
-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
sC
1.0
max
0.8
45.00
0.7 AU
0.6
39.50
0.4
34.00
0.2
28.50
23.00
sR
0.0
17.50
Alfvénic population
e  e 2  v  b 
sC     v b
e e
e e
ev  eb
sR  v b
e e
s C2  s R2  1
-0.2
12.00
-0.4
6.500
min
-0.6
1.000
-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
sC
1.0
max
0.8
45.00
0.6
39.63
0.4
34.25
0.2
28.88
23.50
sR
0.0
18.13
-0.2
12.75
-0.4
7.375
min
-0.6
2.000
-0.8
-1.0
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
sC
0.2
0.4
0.6
0.8
1.0
32
1.0
max
0.8
190.0
0.3 AU
0.6
166.5
0.4
143.0
0.2
119.5
96.00
0.0
sR
Radial evolution of MHD turbulence
in terms of sR and sC (scale of 1hr)
72.50
-0.2
49.00
-0.4
25.50
min
-0.6
2.000
-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
sC
1.0
max
0.8
45.00
0.7 AU
0.6
39.50
0.4
34.00
0.2
28.50
23.00
sR
0.0
17.50
Alfvénic population
e  e 2  v  b 
sC     v b
e e
e e
ev  eb
sR  v b
e e
s C2  s R2  1
-0.2
12.00
-0.4
6.500
min
-0.6
1.000
-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
sC
1.0
max
0.8
45.00
0.6
39.63
0.9 AU
0.4
34.25
28.88
0.2
23.50
sR
0.0
18.13
-0.2
12.75
-0.4
7.375
min
-0.6
2.000
-0.8
-1.0
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
sC
0.2
0.4
0.6
0.8
A new population
appears, characterized
by magnetic energy
excess and low
Alfvénicity
1.0
(Bruno et al., 2007)
33
Similar results obtained by WIND at 1 AU and ULYSSES around 75° and at 2.3AU
Ulysses 1994, polar wind
1.0
max
0.8
70.00
0.6
62.36
54.71
0.4
47.07
sR
0.2
39.42
0.0
31.78
-0.2
24.13
-0.4
16.49
8.844
min
-0.6
1.200
-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
sC
Fluctuations characterized by
magnetic energy excess and
low Alfvénicity
this might be the result of turbulence
evolution or the signature of underlying
advected structure
34
FAST WIND
SLOW WIND
1.0
max
0.8
190.0
0.3 AU
0.6
166.5
0.4
143.0
0.2
119.5
Different situation in
Slow-Wind:
96.00
0.0
sR
0.3 AU
72.50
-0.2
49.00
-0.4
25.50
min
-0.6
• no evolution
2.000
-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
sC
1.0
max
0.8
45.00
0.7 AU
0.6
0.4
39.50
34.00
28.50
0.2
23.00
0.0
sR
0.7 AU
17.50
-0.2
12.00
-0.4
6.500
min
-0.6
1.000
-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
sC
1.0
max
0.8
45.00
0.6
39.63
0.9 AU
0.4
34.25
28.88
0.2
23.50
sR
0.0
18.13
-0.2
12.75
-0.4
7.375
min
-0.6
2.000
-0.8
-1.0
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
sC
0.2
0.4
0.6
0.8
1.0
0.9 AU
• second population
already present at
0.3 AU
In particular: typical case dominated by magnetic energy
magnetic field
velocity
10
50
|B|
vx-vax
8
0
6
-50
4
-100
8
6
100

4
50
0
4x10
5
3x10
5
2x10
5
1x10
5
100
50
10
-50
TP
-100
-9
0
-50
1hr
-100
PTOT
vy-vay
2
vz-vaz
Fluctuations with respect to the average value
100
B-Tp
B-Tp
anticorrelation
PBS
-10
10
51.58746 51.62913 51.67080 51.71247 51.75414 51.79581
time[DoY]
51.58746 51.62913 51.67080 51.71247 51.75414 51.79581
time[DoY]
(Bruno et al., 2007)
36
remarks
Turbulence mostly made of Alfvénic modes and
convected magnetically dominated structures
As the wind expands, convected structures become more
important
It has been shown that the crossing of these structures
affects the selfsimilar character of solar wind fluctuations
and causes anomalous scaling or intermittency (Bruno et al.,
2001)
Effect of intermittency on PDFs
Interplanetary Magnetic Field fluctuations
at three scales
Small scale: stretched exponential
Inertial range: fat tails
Large scale: nearly Gaussian
PDF’s of v and b do not rescale
Effect of intermittency on PDFs
4th order moment or Flatness
to estimate Intermittency
Fτ  S τ4 /(S τ2 )2
where
S  v(t  τ)  v(t) 
p
τ
For a Gaussian statistics Ft=3
“A random function is intermittent at small scales
if the flatness grows without bound at smaller
and smaller scales” (Frisch, 1995)
p
Intermittency along the velocity profile
800
Intermittency strongly depends
on the location within the
stream
BULK SPEED
V [km/sec]
700
600
Fτ  S4τ /(S2τ ) 2
500
400
300
25
44
46
48
50
52
54
56
Magnetic field
58
40
|B|
B(t+)-B(t)
20
47 00 49 12
35
30
15
Flatness
B []
25
10
5
20
15
10
0
5
-5
44
46
48
50
52
54
56
58
0
10
DoY
2
10
3
10
[sec]
4
10
5
Intermittency along the velocity profile
800
Intermittency strongly depends
on the location within the
stream
WIND SPEED
V [km/sec]
700
600
Fτ  S4τ /(S2τ ) 2
500
400
300
25
44
46
48
50
52
54
56
Magnetic field
58
40
|B|
B(t+)-B(t)
20
47 00 49 12
45 12 48 00
35
30
15
Flatness
B []
25
10
5
20
15
10
0
5
-5
44
46
48
50
52
54
56
58
0
10
DoY
2
10
3
10
[sec]
4
10
5
Intermittency along the velocity profile
800
Analyzing long time intervals is
equivalent to mix together solar
wind samples intrinsically
different
WIND SPEED
V [km/sec]
700
600
500
400
300
25
44
46
48
50
52
54
56
Magnetic field
58
40
|B|
B(t+)-B(t)
20
47 00 49 12
45 12 48 00
50 12 53 00
35
30
15
Flatness
B []
25
10
5
20
Inertial range
15
10
0
5
-5
44
46
48
50
52
54
56
58
0
10
DoY
2
10
3
10
[sec]
4
10
5
Effect of intermittency on PDFs
This reflects on the non linear behavior
of the scaling exponent s(p)
Spτ | v(t  τ)  v(t) |p ~ τs(p)
SelfSimilar
Intermittent
Kolmogorov scaling s(p)=p/3
1.8
1.6
1.4
s(p)
1.2
1.0
0.8
0.6
0.4
0.2
1
2
3
p
PDF’s of v and b do not rescale
4
5
PDFs of other parameters can be rescaled
The PDF of , B2, V2, VB2 can be rescaled under the
following change of variable


P(x, )  
Ps (x
, )
(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(b2)
44
Intermittency  anomalous scaling
Studying the anomalous scaling of the different moments can unravel the two
components nature of solar wind fluctuations
(propagating fluctuations vs advected structures)
v//  v  bˆ

(for Alfvénic
fluctuations the scalar
product vanishes)
v  v  v - (v  bˆ )
(Chapman et al., 2008)
RAS Lecture Theatre, Burlington House,
Piccadilly, London, 12 March 2010

Studying the anomalous scaling of the different moments can unravel the two
components nature of solar wind fluctuations
(propagating fluctuations vs advected structures)
Kolmogorov like scaling
v//  v  bˆ

(for Alfvénic
fluctuations the scalar
product vanishes)
v  v  v - (v  bˆ )

Kraichnan like scaling
(Chapman et al., 2008)
v// quasi self-affine scaling
v multifractal scaling
Two possibilities:
1) both components are locally
generated by turbulence in the
presence of a background field
2) v// is a signature of the base of the
corona
RAS Lecture Theatre, Burlington House,
Piccadilly, London, 12 March 2010
Two components invoked also by Bruno et al. (2001):
1) Alfvénic component rather Gaussian
2) Advected structures highly intermittent
Interplanetary Magnetif Field at 0.9 AU
within a high speed stream
10
8
B[]
6
4
Intermittent Component
Gaussian Component
2
0
49.5
50.0
50.5
51.0
51.5
Days
Results obtained using LIM technique
(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.
47
Slow and Fast wind distributions
BZ
Slow wind
BZ Fast wind
Gaussian
(Marsch and Tu, 1994)
Stretched
In high speed solar wind,
perpendicular components are
dominated by stochastic
Alfvénic fluctuations and the
PDFs are nearly Gaussian
48
Two components invoked also by Bruno et al. (2001):
1) Alfvénic component rather Gaussian
2) Advected structures highly intermittent
Interplanetary Magnetif Field at 0.9 AU
within a high speed stream
10
8
B[]
6
4
Intermittent Component
Gaussian Component
2
0
49.5
50.0
50.5
51.0
51.5
Days
Results obtained using LIM technique
(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.
49
Looking at the nature of intermittent events
To measure Intermittency we adopt the Local Intermittency Measure (Farge et al ., 1990)
technique based on wavelet transform
1
 LIM 2 ( , t ) t 
 w4,t t
2
 w ,t t2
2Meneveau
(1991) showed that the Flatness Factor of the wavelet coefficients at a
given scale  is equivalent to the Flatness Factor FF of data at the same scale 
 LIM 2 ( , t ) t 
 w4,t t
2
 w ,t 
2
t
 FF ( )
Thus, values of FF()>3 allow to localize events which lie outside the Gaussian
statistics and cause Intermittency.
1) In Topological Fluid Mechanics, ed H.L.Moffat, Cambridge Univ. Press, 765, 1990
2) Menevau, C., J. Fluid Mech., 232, 469, 1991
Focusing on a magnetic field intermittent event
Using the Local Intermittency Measure
(Farge, 1990)
Minimum Variance Ref. Sys.
A
B
[Bruno et al., 2001]
Fluctuations are Alfvénic on
both sides of the discontinuity
•the discontinuity is 2-D (Ho et
al., 1995)
•there is no mass-flux across it
•it looks like a TD, possibly the
border between adjacent flux
tubes
51
These large rotations were identified as the border between adjacent
flux-tubes
(Bruno et al., 2001)
Local field
6
4
2
Alfvénic fluctuations would cluster within
adjacent flux-tubes along the local
magnetic field direction
Bz
0
-2
-4
6
4
2
-6
-8 6
4
2
0
Bx
-2
-4
-6
-8
0
-2
-4 By
-6
-8
Helios 2, 6sec, 49.628-49.674 (~66min)
52
Several contribution have been given in this
direction in the past years
Similar
pictures
(Mariani et al., 1973; 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)
2D+SLAB
[Tu and Marsch, 1992]
[Bieber, Wanner and
Matthaeus, 1996]
2D+SLAB
(Chang et al., 2002)
Summary #1
•Experimental estimate of the Reynold’s number in the solar wind provide a value of
3105 at 1 AU
•Turbulence is mainly a mixture of random propagating fluctuations (Alfvénic) and
coherent structures (magnetic excess) advected by the wind
•At low frequency, these magnetic structures are responsible for anomalous scaling
(intermittency) of fluctuations and emerge from the Alfvénic background as the wind
expands
•These structures might have:
1.either a solar origin, intimately connected to the topology of the source regions at
the sun
2.or a local (interplanetary) origin due to the non-linear dynamics of the
fluctuations (turbulence evolution)
Is there any link between turbulence in the solar
wind and geomagnetic activity?
Among others, see: Tsurutani and Gonzalez, 1987,
Freeman et al. 2000a,b, Hnat et al. 2002, 2003, 2005,
Vörös et al., 2002, D’Amicis et al., 2004, 2007
Tsurutani and Gonzalez, 1987 suggested that large amplitude interplanetary
Alfvén wave trains might cause intense auroral activities, as a result of the
magnetic reconnection between the southward magnetic field z component and
the magnetopause magnetic fields.
HILDCAAs
This suggestion has been tested on statistical basis for different phases of the solar
cycle (D’Amicis et al., 2007)
Solar wind large scale structure
Solar maximum:
predominance of slow wind
is observed in the ecliptic.
Solar minimum:
fast wind at high latitudes
and an alternation of slow
and fast streams is
observed in the ecliptic.
McComas et al, GRL, 2003
The character of turbulence is different for different phases of the solar cycle
because of the different mixture of fast and slow wind
Geomagnetic response vs wind speed, i.e. vs different kind of
turbulence
D’Amicis et al., 2007 computed average values of AE in correspondence of every square
bin sC-sR at time scale of 1 hour during max and min of solar cycle.
70
63
56
49
42
35
28
21
14
7.0
0.5
0.0
-0.5
sC – sR distributions in the
solar wind
Solar minimum
Alfvénic
fluctuations
e  e
sC  
e  e
-1.0
-1.0
-0.5
ev  eb
sR  v
e  eb
1.0
0.0
0.5
9.0
18
27
36
45
54
63
72
81
90
0.5
1.0
(D'Amicis et al, GRL, 2007)
sC
sR
sR
1.0
0.0
-0.5
• Predominance of Alfvénic fluctuations
propagating away from the Sun
• Tail elongated towards fluctuations
magnetically dominated
Solar maximum
Mixture of Alfvénic
fluct. and structures
-1.0
-1.0
-0.5
Convected
structures
0.0
sC
0.5
1.0
180
High-latitude
geomagnetic
response to solar
wind turbulence
sunspot number
150
AE index
120
90
60
30
0
1996
1998
2000
2002
2004
2006
2008
year
1.0
0.5
AE (nT)
240
Statistical
relationship
between Alfvénic
fluctuations and
auroral activity
Solar maximum
216
192
0.0
192
168
144
0.0
120
96.0
-0.5
96.0
72.0
72.0
-0.5
48.0
48.0
24.0
24.0
-1.0
-1.0
Solar minimum
216
144
120
AE (nT)
240
0.5
sR
sR
168
1.0
-0.5
0.0
sC
0.5
1.0
During solar
maximum large AE
values are found in
non-Alfvénic
regions as well
-1.0
-1.0
-0.5
0.0
0.5
1.0
sC
60
180
Low-latitude
geomagnetic
response to solar
wind turbulence
sunspot number
150
SYM- H
index
120
90
60
30
0
1996
1998
2000
2002
2004
2006
(Wanliss, 2007 suggests that
in future studies the SYMH index be used as a de facto
high-resolution Dst index.)
2008
year
1.0
SYM-H (nT)
-23
-21
0.5
1.0
Solar maximum
Alfvénic
fluctuations
not very
effective on
SYM-H
-18
-14
0.0
sR
sR
-16
-11
SYM-H (nT)
-23
-21
0.5
-18
-16
-14
0.0
-11
-9.2
-9.2
-6.9
-0.5
-6.9
-0.5
-4.6
-4.6
-2.3
-2.3
-1.0
-1.0
Solar minimum
-0.5
0.0
sC
(D'Amicis et al, 2010)
0.5
1.0
Advected
structures
more effective
on SYM-H
-1.0
-1.0
-0.5
0.0
0.5
1.0
sC
61
Summary # 2
Low frequency MHD turbulence (inertial range) seems to be geo-effective in
driving the solar wind-magnetosphere coupling:
1. Alfvénic turbulence plays a role in driving high latitude geomagnetic
activity
2. Advected structures play a role in driving low latitude geomagnetic
activity