Lagrangian acceleration statistics in turbulent flows

TL;DR

This paper demonstrates that a superstatistics-based stochastic model accurately predicts the probability density functions and flatness factors of Lagrangian accelerations in turbulent flows, aligning well with experimental and DNS data.

Contribution

It introduces a superstatistics approach with a log-normal distribution for fluctuating friction, providing analytical predictions that match observed acceleration statistics in turbulence.

Findings

Model predictions agree with experimental acceleration PDFs

Flatness factors from the model match experimental data

The approach suggests universality in small-scale turbulence statistics

Abstract

We show that the probability densities af accelerations of Lagrangian test particles in turbulent flows as measured by Bodenschatz et al. [Nature 409, 1017 (2001)] are in excellent agreement with the predictions of a stochastic model introduced in [C. Beck, PRL 87, 180601 (2001)] 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 hyperflatnes factors for this model and obtain a flatness prediction in good agreement with the experimental data. There is also good agreement with 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.