Revealing intermittency in experimental data with steep power spectra

¹  Laboratoire Matière et Systèmes Complexes (MSC), Université Paris Diderot, CNRS - UMR 7057 10 rue A. Domon & L. Duquet, 75013 Paris, France, EU
²  Université de Lyon, Laboratoire de Physique, CNRS, Ecole Normale Supérieure de Lyon 46 alleé d'Italie, 69007 Lyon, France, EU
³  Université de Lyon, Laboratoire Joliot-Curie, CNRS, Ecole Normale Supérieure de Lyon 46 alleé d'Italie, 69007 Lyon, France, EU

Corresponding author: eric.falcon@univ-paris-diderot.fr

Received: 6 May 2010
Accepted: 3 June 2010

Abstract

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(ω) ~ ω^-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.