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

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.Comment: 23 pages, 13 figures, submitted to Experiments in Fluid

Deriving the respiratory sinus arrhythmia from the heartbeat time series using Empirical Mode Decomposition

Heart rate variability (HRV) is a well-known phenomenon whose characteristics are of great clinical relevance in pathophysiologic investigations. In particular, respiration is a powerful modulator of HRV contributing to the oscillations at highest frequency. Like almost all natural phenomena, HRV is the result of many nonlinearly interacting processes; therefore any linear analysis has the potential risk of underestimating, or even missing, a great amount of information content. Recently the technique of Empirical Mode Decomposition (EMD) has been proposed as a new tool for the analysis of nonlinear and nonstationary data. We applied EMD analysis to decompose the heartbeat intervals series, derived from one electrocardiographic (ECG) signal of 13 subjects, into their components in order to identify the modes associated with breathing. After each decomposition the mode showing the highest frequency and the corresponding respiratory signal were Hilbert transformed and the instantaneous phases extracted were then compared. The results obtained indicate a synchronization of order 1:1 between the two series proving the existence of phase and frequency coupling between the component associated with breathing and the respiratory signal itself in all subjects.Comment: 12 pages, 6 figures. Will be published on "Chaos, Solitons and Fractals

Stochastic analysis of ocean wave states with and without rogue waves

This work presents an analysis of ocean wave data including rogue waves. A stochastic approach based on the theory of Markov processes is applied. With this analysis we achieve a characterization of the scale dependent complexity of ocean waves by means of a Fokker-Planck equation, providing stochastic information of multi-scale processes. In particular we show evidence of Markov properties for increment processes, which means that a three point closure for the complexity of the wave structures seems to be valid. Furthermore we estimate the parameters of the Fokker-Planck equation by parameter-free data analysis. The resulting Fokker-Planck equations are verified by numerical reconstruction. This work presents a new approach where the coherent structure of rogue waves seems to be integrated into the fundamental statistics of complex wave states.Comment: 18 pages, 13 figure