One-dimensional Langevin models of fluid particle acceleration in developed turbulence

Abstract

We make a comparative analysis of some recent one-dimensional Langevin models of the acceleration of a Lagrangian fluid particle in developed turbulent flow. The class of models characterized by random intensities of noises (RIN models) provides a fit to the recent experimental data on the acceleration statistics. We review the model by Laval, Dubrulle, and Nazarenko (LDN) formulated in terms of temporal velocity derivative in the rapid distortion theory approach, and propose its extension due to the RIN framework. The fit of the contribution to fourth order moment of the acceleration is found to be better than in the other stochastic models. We study the acceleration probability density function conditional on velocity fluctuations implied by the RIN approach to LDN type model. The shapes of the conditional distributions and the conditional acceleration variance have been found in a good agreement with the recent experimental data by Mordant, Crawford, and Bodenschatz (2003).