Multifractal scaling of Lagrangian turbulent trajectories using arbitrary order spectral analysis
yongxiang Huang, Francois G. Schmitt, Zhiming Lu, Yulu Liu
UMR LOG-Station marine de Wimereux, France and Shanghai University, China
(Abstract received 07/15/2009 for session B)
ABSTRACT
Hilbert-Huang Transform (or Empirical Mode Decomposition), is a new data analysis technique which was developed 10 years ago by Norden Huang (1998) in order to decompose time series into different scales. We have recently generalized this approach (Huang et al, Europhysics Letters, 2008, 2009) in order to be able to extract multifractal scaling exponents from Eulerian turbulence time series. In the present paper we adapt this methodology to the Lagrangian case. We first theoretically describe how to adapt the previsou methodology to 3D Lagrangian paths, and then show how this can be used to extract multifractal Lagrangian scaling exponents in the framework of turbulent diffusion in homogeneous isotropic turbulence (Kolmogorov-Landau-Novikov’s framework). We also consider the same methodology for Lagrangian passive scalar measurements.
We then perform data analyses in this framework. For this, we consider two different data bases: experimental measurements of Lagrangian diffusion in a homogeneous turbulent situation (using polystyrene particles), performed by Ott and Mann (2000) and several oceanic Lagrangian databases. We show how the new methodology using arbitrary order Hilbert-Huang spectral analysis is able to better extract scaling exponents, on a wider range of scales, compared to the more classical structure functions analysis.
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