The PDF of fluid particle acceleration in turbulent flow with underlying normal distribution of velocity fluctuations
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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, $β=\exp[u]$, of the fluctuating parameter $β$, 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.
RevTeX4, 4 pages, twocolumn, no figures. Revised version, to appear in Phys. Lett. A (2003)
RevTeX4, 4 pages, twocolumn, no figures. Revised version, to appear in Phys. Lett. A (2003)