The PDF of fluid particle acceleration in turbulent flow with underlying normal distribution of velocity fluctuations

TL;DR

This paper derives a general form for the distribution of fluid particle acceleration in turbulence, assuming Gaussian velocity fluctuations, and shows that a log-normal model aligns well with experimental data.

Contribution

It introduces a formal procedure to specify the marginal distribution of acceleration in turbulent flow using Langevin equations and Gaussian velocity assumptions, reproducing the log-normal distribution.

Findings

Log-normal distribution fits experimental acceleration data well.

Derived a general form for acceleration distribution under Gaussian velocity fluctuations.

Discussed potential refinements to the log-normal turbulence model.

Abstract

We describe a formal procedure to obtain and specify the general form of a marginal distribution for the Lagrangian acceleration of fluid particle in developed turbulent flow using Langevin type equation and the assumption that velocity fluctuation $u$ follows a normal distribution with zero mean, in accord to the Heisenberg-Yaglom picture. For a particular representation, $\beta=\exp[u]$, of the fluctuating parameter $\beta$, we reproduce the underlying log-normal distribution and the associated marginal distribution, which was found to be in a very good agreement with the new experimental data by Crawford, Mordant, and Bodenschatz on the acceleration statistics. We discuss on arising possibilities to make refinements of the log-normal model.