Revealing intermittency in experimental data with steep power spectra

E. Falcon1, S. Roux2 & B. Audit3
1MSC, University Paris Diderot, CNRS - UMR 7057, 75 013 Paris, France
2University of Lyon, Lab. de Physique, Ecole Normale Supérieure de Lyon, CNRS - UMR 5672, Lyon, France
3University of Lyon, Lab. Joliot-Curie, Ecole Normale Supérieure de Lyon, CNRS - UMR 5672, Lyon, France


EPL 90, 50007 (2010)



The statistics of signal increments are commonly used in order to test for possible intermittent properties in experimental or synthetic data. However, for signals with steep power spectra [i.e., E(f) ~ f - n with n  3], the increments are poorly informative and the classical phenomenological relationship between the scaling exponents of the second-order structure function and of the power spectrum does not hold. We show  that in these conditions the relevant quantities to compute are the second or higher degree differences of the signal. Using this statistical framework to analyze a synthetic signal and experimental data of wave turbulence on a fluid surface, we accurately characterize intermittency of these data with steep power spectra. The general application of this methodology to study intermittency of experimental signals with steep power spectra is discussed. 

PACS : 05.40.-a - Fluctuation phenomena, random processes, 47.27.-i   - Turbulent flows, 47.35.+i  - Hydrodynamic waves

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