Skewness of probability density functions of fluid particle acceleration in developed turbulence

Within the framework of one-dimensional Laval-Dubrulle-Nazarenko type model for the Lagrangian acceleration in developed turbulence studied in the work [A.K. Aringazin and M.I. Mazhitov, cond-mat/0305186] we focus on the effect of correlation between the multiplicative noise and the additive one which models the relationship between the stretching and vorticity, and can be seen as a skewness of the probability density function of some acceleration component. The skewness of the acceleration distribution in the laboratory frame of reference should be zero in the ideal case of statistically homogeneous and isotropic developed turbulent flows but when considering acceleration component aligned to fluid particle trajectories it is of much importance in understanding of the cascade picture in the three-dimensional turbulence related to Kolmogorov four-fifths law. We illustrate the effect of nonzero cross correlation parameter $\lambda$. With $\lambda=-0.005$ the transverse ($x$) acceleration probability density function turns out to be in good agreement with the recent experimental data by Mordant, Crawford, and Bodenschatz. In the Random Intensity of Noise (RIN) approach, we study the conditional probability density function and conditional mean acceleration assuming the additive noise intensity to be dependent on velocity fluctutions.