  Modeling statistical properties of motion of a Lagrangian particle advected
by a high-Reynolds-number flow is of much practical interest and complement
traditional studies of turbulence made in Eulerian framework. The strong and
nonlocal character of Lagrangian particle coupling due to pressure effects
makes the main obstacle to derive turbulence statistics from the
three-dimensional Navier-Stokes equation; motion of a single fluid-particle is
strongly correlated to that of the other particles. Recent breakthrough
Lagrangian experiments with high resolution of Kolmogorov scale have motivated
growing interest to acceleration of a fluid particle. Experimental stationary
statistics of Lagrangian acceleration conditioned on Lagrangian velocity
reveals essential dependence of the acceleration variance upon the velocity.
This is confirmed by direct numerical simulations. Lagrangian intermittency is
considerably stronger than the Eulerian one. Statistics of Lagrangian
acceleration depends on Reynolds number. In this review we present description
of new simple models of Lagrangian acceleration that enable data analysis and
some advance in phenomenological study of the Lagrangian single-particle
dynamics. Simple Lagrangian stochastic modeling by Langevin-type dynamical
equations is one the widely used tools. The models are aimed particularly to
describe the observed highly non-Gaussian conditional and unconditional
acceleration distributions. Stochastic one-dimensional toy models capture main
features of the observed stationary statistics of acceleration. We review
various models and focus in a more detail on the model which has some deductive
support from the Navier-Stokes equation. Comparative analysis on the basis of
the experimental data and direct numerical simulations is made.
