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Article Dans Une Revue Physical Review Applied Année : 2017

Extremal-point density of scaling processes: From fractional Brownian motion to turbulence in one dimension

Yongxiang Huang
  • Fonction : Auteur
Lipo Wang
Xiaobo Zheng
  • Fonction : Auteur
Nan Jiang
  • Fonction : Auteur

Résumé

In recent years several local extrema-based methodologies have been proposed to investigate either the nonlinear or the nonstationary time series for scaling analysis. In the present work, we study systematically the distribution of the local extrema for both synthesized scaling processes and turbulent velocity data from experiments. The results show that for the fractional Brownian motion (fBm) without intermittency correction the measured extremal-point-density (EPD) agrees well with a theoretical prediction. For a multifractal random walk (MRW) with the lognormal statistics, the measured EPD is independent of the intermittency parameter μ, suggesting that the intermittency correction does not change the distribution of extremal points but changes the amplitude. By introducing a coarse-grained operator, the power-law behavior of these scaling processes is then revealed via the measured EPD for different scales. For fBm the scaling exponent ξ(H) is found to be ξ(H)=H, where H is Hurst number, while for MRW ξ(μ) shows a linear relation with the intermittency parameter μ. Such EPD approach is further applied to the turbulent velocity data obtained from a wind tunnel flow experiment with the Taylor scale λ-based Reynolds number Reλ=720, and a turbulent boundary layer with the momentum thickness θ based Reynolds number Reθ=810. A scaling exponent ξ≃0.37 is retrieved for the former case. For the latter one, the measured EPD shows clearly four regimes, which agrees well with the corresponding sublayer structures inside the turbulent boundary layer.

Domaines

Océanographie

Dates et versions

hal-01572028 , version 1 (04-08-2017)

Identifiants

Citer

Yongxiang Huang, Lipo Wang, François G Schmitt, Xiaobo Zheng, Nan Jiang, et al.. Extremal-point density of scaling processes: From fractional Brownian motion to turbulence in one dimension. Physical Review Applied, 2017, 96:012215, ⟨10.1103/PhysRevE.96.012215⟩. ⟨hal-01572028⟩
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