Lagrangian singleparticle turbulent statistics through the HilbertHuang transform
Abstract
The HilbertHuang transform is applied to analyze singleparticle 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 ωconditioned statistical moments of the C_{i} modes, named qorder Hilbert spectra (HS). We show that such quantities have enhanced scaling properties as compared to traditional Fourier transform or correlationbased (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 secondorder HS, displays a linear scaling in time in the inertial range, as expected from a dimensional analysis. We also measure highorder moment scaling exponents in a direct way, without resorting to the extended selfsimilarity 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 [Phys. Rev. Lett.PRLTAO0031900710.1103/PhysRevLett.93.064502 93, 064502 (2004)].
 Publication:

Physical Review E
 Pub Date:
 April 2013
 DOI:
 10.1103/PhysRevE.87.041003
 arXiv:
 arXiv:1212.5741
 Bibcode:
 2013PhRvE..87d1003H
 Keywords:

 47.27.Gs;
 02.50.r;
 47.27.Jv;
 89.75.Da;
 Isotropic turbulence;
 homogeneous turbulence;
 Probability theory stochastic processes and statistics;
 HighReynoldsnumber turbulence;
 Systems obeying scaling laws;
 Physics  Fluid Dynamics;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 5 pages, 5 figures