A Statistical Theory on the Turbulent Diffusion of Gaussian Puffs.

The relative diffusion of a one-dimensional Gaussian cloud of particles is related to a two-particle covariance func-tion Rabs(?ij'T) = U(XJ_( t) )U(XJ_( t-T)-g^j ) in a homogeneous and stationary field of turbulence. This two-particle covariance function expresses the velocity correlation between one par-ticle (i) which at time t is in the position x^, and another (j), which at the previous time t-x is displaced the fixed distance Sij relative to xi(t-x). For £ij = 0f Rabs reduces to the Lagrangian covariance function of a single particle. On the other handf setting the time lag T equal to zero, Rabs becomes a pure Eulerian (fixed point) covariance function.

For diffusion times that are small compared to the Lagrangian integral time scale of the turbulencef simple expressions are derived for the growth of the standard deviation a(t) of the cloud by assuming that the wave number spectrum corresponding