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

¹  Université des Sciences et Technologies de Lille - Lille 1, CNRS, Laboratory of Oceanology and Geosciences, UMR 8187 LOG - 62930 Wimereux, France, EU
²  Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University - 200072 Shanghai, China

Corresponding authors: francois.schmitt@univ-lille1.fr zmlu@staff.shu.edu.cn

Received: 23 May 2008
Accepted: 16 October 2008

Abstract

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.