Separation between coherent and turbulent fluctuations. What can we learn from the Empirical Mode Decomposition?

TL;DR

This paper evaluates the effectiveness of Empirical Mode Decomposition in separating turbulent velocity signals from perturbations, proposing a criterion and rejection method to recover original signals with high accuracy, especially for mono-component and broad-range perturbations.

Contribution

It introduces a new resemblance criterion and a rejection procedure for Empirical Mode Decomposition to effectively distinguish and recover turbulent signals from perturbations.

Findings

High accuracy in recovering signals with mono-component perturbations.

Effective separation of signals even with broad-range perturbations.

Discrepancies occur when perturbation frequencies overlap energy-containing eddies.

Abstract

The performances of a new data processing technique, namely the Empirical Mode Decomposition, are evaluated on a fully developed turbulent velocity signal perturbed by a numerical forcing which mimics a long-period flapping. First, we introduce a "resemblance" criterion to discriminate between the polluted and the unpolluted modes extracted from the perturbed velocity signal by means of the Empirical Mode Decomposition algorithm. A rejection procedure, playing, somehow, the role of a high-pass filter, is then designed in order to infer the original velocity signal from the perturbed one. The quality of this recovering procedure is extensively evaluated in the case of a "mono-component" perturbation (sine wave) by varying both the amplitude and the frequency of the perturbation. An excellent agreement between the recovered and the reference velocity signals is found, even though some discrepancies are observed when the perturbation frequency overlaps the frequency range corresponding to the energy-containing eddies as emphasized by both the energy spectrum and the structure functions. Finally, our recovering procedure is successfully performed on a time-dependent perturbation (linear chirp) covering a broad range of frequencies.