  The motion of a particle carried by a liquid is described by the differential
equation equating the velocity of the particle at time t to the the Eulerian
velocity field at time t and at the location of the particle at that time.
Assuming the velocity field to be random with a stationary, isotropic,
translational invariant, zero mean distribution, the Lagrangian velocity
correlation of the particle can be expressed in terms of the Eulerian
correlations and the characteristic function of the probability distribution of
the end point of the trajectory at time t, where the particle is taken to be at
the origin at time 0. This is a result of a decoupling, which is exact to
leading order in the volume of the system.
