An amplitude-frequency study of turbulent scaling intermittency using Empirical Mode Decomposition and Hilbert Spectral Analysis

Yongxiang Huang (1, 2) , François G Schmitt (1) , Zhiming Lu (2) , Yulu Liu (2)

1 LOG - Laboratoire d’Océanologie et de Géosciences (LOG) - UMR 8187
2 SIAMM - Shanghai Institute of Applied Mathematics and Mechanics

Hilbert-Huang transform is a method that has been introduced recently to decompose nonlinear, nonstationary time series into a sum of different modes, each one having a characteristic frequency. Here we show the first successful application of this approach to homogeneous turbulence time series. We associate each mode to dissipation, inertial range and integral scales. We then generalize this approach in order to characterize the scaling intermittency of turbulence in the inertial range, in an amplitude-frequency space. The new method is first validated using fractional Brownian motion simulations. We then obtain a 2D amplitude-frequency representation of the pdf of turbulent fluctuations with a scaling trend, and we show how multifractal exponents can be retrieved using this approach. We also find that the log-Poisson distribution fits the velocity amplitude pdf better than the lognormal distribution.

Mots clés: Time series analysis; Stochastic analysis; Isotropic turbulence; homogeneous turbulence; Fractals in fluid dynamics

Domaines: Analyse de données, Statistiques et Probabilités [physics.data-an]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Mécanique statistique [cond-mat.stat-mech]

Yongxiang Huang, François G Schmitt, Zhiming Lu, Yulu Liu. An amplitude-frequency study of turbulent scaling intermittency using Empirical Mode Decomposition and Hilbert Spectral Analysis. EPL - Europhysics Letters, 2008, 84 (4), pp.40010. ⟨10.1209/0295-5075/84/40010⟩. ⟨hal-00449063⟩