title: Lagrangian single-particle turbulent statistics through the Hilbert-Huang transform.
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 C(i)(t) and of their instantaneous frequency ω(i)(t). On the basis of this decomposition we define the ω-conditioned statistical moments of the C(i) 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)].
authors.affiliation: Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, People's Republic of China. yongxianghuang@gmail.com
authors.forename: Yongxiang
authors.initials: Y
authors.lastname: Huang
authors.forename: Luca
authors.initials: L
authors.lastname: Biferale
authors.forename: Enrico
authors.initials: E
authors.lastname: Calzavarini
authors.forename: Chao
authors.initials: C
authors.lastname: Sun
authors.forename: Federico
authors.initials: F
authors.lastname: Toschi