|
|
|
|
K. Seki, K. Kitahara, and G. Nicolis
[Physica A, Vol. 209, pp. 369-384, 1994]
Anomalous relative diffusion in turbulent media provides a striking example of a phenomenon exhibiting long-range correlations. In the present work, we investigate relative diffusion of a pair of initially close particles on the basis of a Langevin equation in which random forces are spatially correlated. We do not specify the particular form of the spatial correlation of the random force except by imposing translational invariance. Under the assumption of Gaussian random force a nonlinear evolution equation describing the mean square distance of initially close tagged particles in turbulent medium is obtained. The equation is the same as that derived for a turbulent plasma by Misguich and Balescu using renormalized kinetic theory. The approach is extended to incorporate stable drift in connection with the diffusion of macro particles in a turbulent fluid. The initial t3 and intermediated exponential growth of the mean square distance subsist even under the presence of stable drift in agreement with many confirmed observations.