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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. 2. 3. 4. 5. 6. 7. 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 ? • • • • 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).