Revealing intermittency in experimental data with steep power
spectra

E. Falcon^{1}, S. Roux^{2} & B.
Audit^{3}

^{1}MSC, University
Paris Diderot, CNRS - UMR 7057, 75 013 Paris, France ^{2}University of Lyon, Lab. de Physique, Ecole Normale
Supérieure de Lyon, CNRS - UMR 5672,
Lyon, France ^{3}University of Lyon, Lab. Joliot-Curie, Ecole Normale
Supérieure de Lyon, CNRS - UMR 5672,
Lyon, France

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.