fluid parcel trajectories they cross at any given time; from Eqn. (4.7): $\langle |\z^\smalP(t|\x,-\infty)-\z(t|\x,-\infty)|^2\rangle
\sim (u_T\tau_S)^2\sim \Ckol\flux^\frac{2}{3}k_0^{-\frac{2}{3}}\tau_S^2$. We thus introduce the localization length $S_l$: $$S_l=\Ckol^\frac{1}{2}\flux^\frac{1}{3}k_0^{-\frac{1}{3}}\tau_S
\eqno(4.8)$$ What happens is that the velocity difference $\v^\smalP-\u^\smalP$ obeys a relaxation equation with a forcing which is a time derivative; from Eqn. (4.2): $\frac{\d}{\d t}(\v^\smalP-\u^\smalP)+\tau_S^{-1}(\v^\smalP-\u^\smalP)=-\dot\u^\smalP$. The frequency spectrum of $\v^\smalP-\u^\smalP$ does not have therefore the small frequency singularity necessary for long time divergence. The localization length $S_l$ will appear to play a fundamental role in the production both of concentration fluctuations and of corrections to the velocity correlation time. (Of course, to higher order in $\rho^{-1}$, the relative separation of fluid parcels sets in and localization is destroyed; $S_l$ becomes then, that part of trajectory separation which remains after the Richardson diffusion contribution is subtracted out).

In the absence of gravity, beside the integral scale dependent localization length $S_l$, three more scales, which, if $\tau_S\ll\tau_L$, are purely inertial, can be obtained combining $\tau_S$, the crossing time of an eddy by a solid particle, the eddy lifetime and the eddy turn-over time. We have the size $S$ of an eddy whose lifetime equals $\tau_S$: $\gamma_{S^{-1}}\tau_S\sim 1$; the size $S_c$ of an eddy that is crossed 