The conditional mean acceleration of fluid particle in developed turbulence

Using the random intensity of noise (RIN) approach to the one-dimensional Laval-Dubrulle-Nazarenko type model for the Lagrangian acceleration in developed turbulence [cond-mat/0305186, cond-mat/0305459] we study the probability density function and mean acceleration conditional on velocity fluctuations. The additive noise intensity and the cross correlation between the additive and multiplicative noises are assumed to be dependent on velocity fluctuations in an exponential way. The obtained fit results are found to be in a good qualitative agreement with the recent experimental data on the conditional acceleration statistics by Mordant, Crawford, and Bodenschatz. The fit to the observed conditional mean acceleration is of pure illustrative character which is performed to study influence of variation of the cross correlation parameter on the shape of conditional acceleration distribution and conditional acceleration variance. The conditional mean acceleration should be zero for homogeneous isotropic turbulence. The observed conditional mean acceleration increases for bigger velocity fluctuation amplitude and is associated to anisotropy of the studied flow.