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

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.