TY - JOUR

T1 - Lagrangian single-particle turbulent statistics through the Hilbert-Huang transform

AU - Huang, Y.

AU - Biferale, L.

AU - Calzavarini, E.

AU - Sun, C.

AU - Toschi, F.

PY - 2013

Y1 - 2013

N2 - 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)].

AB - 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)].

U2 - 10.1103/PhysRevE.87.041003

DO - 10.1103/PhysRevE.87.041003

M3 - Article

C2 - 23679366

VL - 87

SP - 041003-1/5

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 4

M1 - 041003

ER -