Lagrangian single particle turbulent statistics through the Hilbert-Huang Transform

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, \omega_i(t). On the basis of this decomposition we define the \omega-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 (i.e. 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 Hilbert spectrum, displays a linear scaling in ! in the inertial range, as expected from dimensional analysis and never observed before. We present also results on high order moments and we measure their scaling exponents in a direct way, i.e., without resorting the Extended Self Similarity procedure. This leads to new estimate of the Lagrangian structure function exponents which are consistent with the multifractal prediction in the Lagrangian frame as proposed in [Biferale et al., Phys. Rev. Lett. 93, 64502 (2004)].