### 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 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.

Original language | English |
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Article number | 041003 |

Number of pages | 5 |

Journal | Physical review E: Statistical, nonlinear, and soft matter physics |

Volume | 87 |

DOIs | |

Publication status | Published - 2013 |

### Keywords

- METIS-295854
- IR-89916

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## Cite this

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*, [041003]. https://doi.org/10.1103/PhysRevE.87.041003