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 new 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 a clear empirical evidence that the energy-like quantity, i.e. the second-order HS, displays a linear scaling in time in the inertial range, as expected from dimensional analysis and never observed before. We also measure high order moment scaling exponents in a direct way, without resorting the Extended Self Similarity (ESS) procedure. This leads to a new estimate of the Lagrangian structure functions exponents which are consistent with the multifractal prediction in the Lagrangian frame as proposed in [Biferale et al., Phys. Rev. Lett. vol. 93, 064502 (2004)].