2017/07/17 by Yongxiang Huang, Lipo Wang, François G. Schmitt +4
Economics, Econometrics and Finance · Environmental Science · Mathematics · Physics and Astronomy · #Brownian motion #Combinatorics #Complex Systems and Time Series Analysis #Dimension (graph theory) #Exponent #Financial Risk and Volatility Modeling #Fractional Brownian motion #Geometry #Hurst exponent #Hydrology and Drought Analysis #Intermittency #Mathematical analysis #Mathematics #Maxima and minima #Physics #Quantum mechanics #Random walk #Reynolds number #Scaling #Statistical physics #Statistics #Turbulence #cond-mat.stat-mech #physics.flu-dyn
paper · pdf · doi:10.1103/physreve.96.012215
published as published in Physical Review E, 2017, 96:012215 · 26 pages with 19 figures
openalex publication_date 2017/07/17 · arxiv created 2018/09/20 · arxiv updated 2018/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.