Revealing intermittency in experimental data with steep power spectra

TL;DR

This paper introduces a new method using higher degree differences to detect intermittency in signals with steep power spectra, where traditional increment analysis fails, demonstrated on synthetic and wave turbulence data.

Contribution

It proposes a novel statistical approach based on higher degree differences for analyzing intermittency in signals with steep power spectra, overcoming limitations of classical methods.

Findings

Higher degree differences effectively reveal intermittency in steep spectrum signals

The method accurately characterizes intermittency in synthetic and experimental wave turbulence data

Classical increment analysis is inadequate for signals with $n \,\geq\, 3$ in the power spectrum

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., $E(\omega) \sim \omega^{-n}$ with $n \geq 3$], 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.