turbulence in the magnetosphere studied with cluster data : evidence of intermittency lamy h. 1,...
TRANSCRIPT
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
1. Turbulence/Intermittency2. Turbulence in the Cusp 3. CLUSTER data4. Probability Distribution Functions (PDF)5. Flatness6. Correlation coefficients (auto and cross)7. 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)
Richardson cascade
• Self-similarity
• Localness of interactions
driving scale
inertial scales
dissipation scale
Two main hypotheses :
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 p-model, Meneveau & Sreenivasan 1987)
Turbulence in the magnetosphere
• Energy transfer from large scales to kinetic scales ?
• Mass and momentum transfer from one region of the magnetosphere to another
(Goldstein 2005)
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
Inner magnetosphere Cusp and crossings regions Magnetosheath
Densities from the WHISPER experiment
How can we detect/quantify intermittency ?
• 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 Scaled PDFsB2
PDFs in the cusp region
Non-scaled PDFs Scaled PDFsB2
PDFs in the magnetosheath
Non-scaled PDFs Scaled PDFsB2
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, non-gaussian 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 non-gaussian rescaling of the PDFs (Hnat et al. 2002) + multi-fractal analysis (investigations in progress).