Lagrangian single-particle turbulent statistics through the Hilbert-Huang transform

Y. Huang, L. Biferale, E. Calzavarini, C. Sun, F. Toschi

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35 Citations (Scopus)
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Abstract

The Hilbert-Huang transform is applied to analyze single-particle Lagrangian velocity data from numerical simulations of hydrodynamic turbulence. The velocity trajectory is described in terms of a set of intrinsic mode functions Ci(t) and of their instantaneous frequency ¿i(t). On the basis of this decomposition we define the ¿-conditioned statistical moments of the Ci modes, named q-order Hilbert spectra (HS). We show that such quantities have enhanced scaling properties as compared to traditional Fourier transform- or correlation-based (structure functions) statistical indicators, thus providing better insights into the turbulent energy transfer process. We present clear empirical evidence that the energylike quantity, i.e., the second-order HS, displays a linear scaling in time in the inertial range, as expected from a dimensional analysis. We also measure high-order moment scaling exponents in a direct way, without resorting to the extended self-similarity procedure. This leads to an estimate of the Lagrangian structure function exponents which are consistent with the multifractal prediction in the Lagrangian frame as proposed by Biferale et al. [ Phys. Rev. Lett. 93 064502 (2004)].
Original languageEnglish
Article number041003
Pages (from-to)041003-1/5
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume87
Issue number4
DOIs
Publication statusPublished - 2013

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