  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.
