Lagrangian single particle turbulent statistics through the Hilbert-Huang Transform

TL;DR

This paper applies the Hilbert-Huang transform to Lagrangian turbulence data, revealing enhanced scaling properties and providing new insights into energy transfer and multifractal behavior in turbulence.

Contribution

It introduces Hilbert Spectra for analyzing turbulent velocity data, demonstrating improved scaling and direct measurement of structure function exponents.

Findings

Second-order Hilbert Spectrum shows linear inertial range scaling.

High-order exponents measured directly without ESS.

Results align with multifractal predictions for Lagrangian turbulence.

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, \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 (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)].