Transcript Magnetopause turbulence studied with CLUSTER data

Turbulence in the magnetosphere
studied with CLUSTER data :
evidence of intermittency
Lamy H.1, Echim M.1,2, Darrouzet F.1,
Lemaire J.3, Décréau P.4, Dunlop M.5
1 Belgian Institute of Space Aeronomy, Brussels, Belgium
2 Institute of Space Sciences, Bucharest, Romania
3 Center for Space Radiations, Louvain-La-Neuve, Belgium
4 LPCE/CNRS, University of Orléans, France
5 Rutherford Appleton Laboratory, United Kingdom
Outline of the talk
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Turbulence/Intermittency
Turbulence in the Cusp
CLUSTER data
Probability Distribution Functions (PDF)
Flatness
Correlation coefficients (auto and cross)
Conclusions & Perspectives
What is turbulence ?
• A non-linear phenomenom resulting from the interaction
between waves and eddies of many different scales.
• In a turbulent regime, fluid and plasma parameters vary
randomly in time and space
Statistical approach
Classical turbulence (Kolmogorov 41)
driving scale
inertial scales
dissipation scale
Richardson cascade
• Self-similarity
Two main hypotheses :
• Localness of interactions
Self-similarity/Intermittency
• Self-similar fluctuations : if we magnify an arbitrary part, the
statistical properties will be identical
• Intermittent fluctuations : alternance of intervals with high
activity with quiet intervals
Brownian motion is
self-similar
The Devil’s staircase is
intermittent
Several models of intermittency
• Smaller eddies are less and less space-filling (ex : the 
model, Frisch 1995)
• The energy transfer rate is scale-dependent (ex : the pmodel, Meneveau & Sreenivasan 1987)
Turbulence in the magnetosphere
(Goldstein 2005)
• Energy transfer from large scales to kinetic scales ?
• Mass and momentum transfer from one region of the
magnetosphere to another
Turbulence in the cusp region
• Cluster spacecraft allow to distinguish between temporal
and spatial fluctuations
• Nykyri et al. (2004) : using magnetometer data from
Cluster, they find evidence that the cusp contains
magnetic turbulence.
• Sundkvist et al. (2005) : discovery of short-scale vortices
in the cusp region  another channel to transport plasma
particles and energy through the magnetospheric
boundary layers.
CLUSTER data
• Outbound pass on February 26, 2001 [3:30:00 – 7:00:00 UT]
• High resolution Magnetic Field (MF) data from the FGM
magnetometer : 8 samples/sec for [3:30:00 – 5:30:00 UT] and 3
samples/sec for [5:30:00 – 7:00:00 UT]
• A background MF (IGRF + external Tsyganenko 2001) has been
subtracted from the data before analyzing the fluctuations.
• Three distinct regions along the spacecraft trajectory are
considered
CLUSTER data
Densities from
the WHISPER
experiment
Inner magnetosphere
Cusp and crossings regions
Magnetosheath
How can we detect/quantify intermittency ?
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Probability distribution functions (PDFs)
Flatness
Multi-fractal analysis
Continuous Wavelet Transform
Probability density functions (PDFs)
• PDF = histogram of the fluctuating field P(t)
P(t,) = P(t+) – P(t)
for a given value  of the temporal scale. ( P=Bx,By,Bz or B2 )
•  is the time that separates two observations of a fluctuating
component :
 = t . 2n
where t is the time resolution of the data.
• Intermittency is associated with increasing departure of PDFs
from gaussianity when the scale  decreases.
• Number of points << than in SW data  statistics is good
only up to ~  5
PDFs in the inner magnetosphere
Non-scaled PDFs
B2
Scaled PDFs
PDFs in the cusp region
Non-scaled PDFs
B2
Scaled PDFs
PDFs in the magnetosheath
Non-scaled PDFs
B2
Scaled PDFs
FLATNESS
• The flatness F is related to higher moments of the
fluctuations :
F =<P(t,)4> / (<P(t,)2>)2
< > = mean on all data considered
• A fluctuating parameter is intermittent if F increases
when considering smaller scales
• If F remains more or less constant whatever the scale,
the fluctuations are self-similar
• F = 3 for Gaussian fluctuations
FLATNESS IN THE INNER MAGNETOSPHERE
FLATNESS IN THE CUSP REGION
FLATNESS IN THE MAGNETOSHEATH
CORRELATION COEFFICIENTS
= cross correlation coefficient between
Pi and Pj for the time-lag 
Auto-correlation when i = j
• The Magnetic Field will be correlated with itself within a
turbulent eddy and uncorrelated outside the eddy.
• The value of  for which the auto-correlation coefficient =
1/e gives the temporal scale size of the eddy. The length of
the eddy can then be deduced from the flow speed of the
plasma
CORRELATION COEFFICIENTS
• Cluster 1 & 4
• Comp. Bz
• Complete data
Dynamic
nature of the
turbulent
eddies
COMPARISON MACRO/MICRO-SCALES
CLUSTER 1 & 4
CONCLUSIONS & PERSPECTIVES
• PDFs : gaussian in the inner magnetosphere, nongaussian in the cusp and magnetosheath
• Flatness : F takes values close to 3 in the magnetosphere
and strongly increases with decreasing scale in the cusp
and magnetosheath region
• These results suggest the presence of intermittent
turbulence in the cusp and magnetosheath
• Correlation analysis : existence of structures with scales
comparable to the satellite separation distance.
Structures with smaller scales exist as well, suggesting
non self-similarity.
• To test this hypotheses more quantitavely  nongaussian rescaling of the PDFs (Hnat et al. 2002) +
multi-fractal analysis (investigations in progress).