2002/12/23 by Christian Beck · 5 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Acceleration #Advanced Statistical Methods and Models #Classical mechanics #Complex Systems and Time Series Analysis #Flatness (cosmology) #Lagrangian #Mathematical analysis #Mathematics #Mechanics #Physics #Statistical Mechanics and Entropy #Statistical mechanics #Statistical physics #Statistics #Turbulence #Universality (dynamical systems) #cond-mat.stat-mech #physics.flu-dyn
paper · pdf · doi:10.1209/epl/i2003-00498-4
10 pages, 2 figures
arxiv created 2002/12/23 · openalex publication_date 2003/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that the probability densities of accelerations of Lagrangian test particles in turbulent flows as measured by Bodenschatz et al. ( Nature , 409 (2001) 1017) are in excellent agreement with the predictions of a stochastic model introduced in Beck, Phys. Rev. Lett. , 87 (2001) 180601 if the fluctuating friction parameter is assumed to be log-normally distributed. In a generalized statistical mechanics setting, this corresponds to a superstatistics of log-normal type. We analytically evaluate all hyperflatness factors for this model and obtain predictions in good agreement with the experimental data and the DNS data of Gotoh et al. We relate the model to a generalized Sawford model with fluctuating parameters, and discuss a possible universality of the small-scale statistics.