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.
|Number of pages||5|
|Journal||Physical review E: Statistical, nonlinear, and soft matter physics|
|Publication status||Published - 2013|
Huang, Y., Biferale, L., Calzavarini, E., Sun, C., & Toschi, F. (2013). Lagrangian single-particle turbulent statistics through the Hilbert-Huang transform. Physical review E: Statistical, nonlinear, and soft matter physics, 87, . https://doi.org/10.1103/PhysRevE.87.041003