A general LS model is considered covering motion of any number of particles. 
The corresponding one-particle motion model includes Markov models of any order 
as a partial case. In a recent work by R. Mikulevicius and B. Rozovskii , a 
rigorous derivation of stochastic Navier-Stokes and Euler equations for the 
corresponding Eulerian velocity was presented. These equations are natural 
extensions of the classical equation of Fluid Mechanics to the case when the 
fluid particles are subject to short-time turbulence. The existence and 
uniquiness conditions for the corresponding Eulerian velocity field were 
given in terms of the Lagrangian drift and diffusion tensor. In this talk 
we will discuss how some popular hydrodynamic LS models introduced by 
different authors (Thomson, Reynolds, Pedrizzetti and Novikov) relate to 
this general approach. We also discuss the Lagrangian data assimilation 
problem in context of our findings.