Revealing intermittency in experimental data with steep power spectra

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 $n\ge 3$], 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.

References in corpus (5)

• Observation of gravity-capillary wave turbulence
• Observation of intermittency in wave turbulence
• Vorticity statistics in the two-dimensional enstrophy cascade
• Multiscaling and Structure Functions in Turbulence: An Alternative Approach
• Inverse velocity statistics in two dimensional turbulence

Cited by in corpus (8)

• Experiments in Surface Gravity-Capillary Wave Turbulence
• The NANOGrav Nine-Year Data Set: Excess Noise in Millisecond Pulsar Arrival Times
• Role of the basin boundary conditions in gravity wave turbulence
• Wave turbulence and intermittency in directional sea states
• Instability onset and scaling laws of an autooscillating turbulent flow in a complex plasma
• One-dimensional hydrodynamic model generating a turbulent cascade
• Multi-time structure functions and the Lagrangian scaling of turbulence
• Generation of intermittent gravitocapillary waves via parametric forcing