scale fixed by those eddies which have decay time $\tau_S$. Hence, for $\rho$ large, the fluctuating part of trajectory separation remains small on the scale of these eddies. Furthermore, when either $u_Gt>\delta z(t|\x+\u_Gt,\x)$, or $\gamma_{|u_Gt|^{-1}}t> 1$, in other words, when either $\frac{\Ckol^\frac{3}{2}\flux t}{u_G^2} < 1 $ or $\frac{\Ckol^\frac{3}{2}\flux t}{u_G^2}>\rho^{-3}$ (provided $\rho> 1$, one of the two conditions is always satisfied), it is possible to approximate $\z(t|\x,0)+\u_Gt\simeq \z(t|\x+\u_Gt,0)$.

To lowest order we have therefore: $$\u(\z^\smalP(t|\x,0),t)=\u(\u_Gt+\z(t|\x,0),t)=\u^\smalL(\x+\u_Gt,t)
\eqno(4.3)$$ We obtain immediately the fluctuation amplitude of the velocity difference between solid and fluid particle at a given position. From Eqns. (4.2-3) we can write: $$\v^\smalP(\x,t)=\int\frac{\d^2k}{(2\pi)^2}\int_{-\infty}^t\frac{\d\tau}{\tau_S}\u^\smalL_\k(\tau)
\exp(-\frac{t-\tau}{\tau_S}+\i\k\cdot\x)
\eqno(4.4)$$ and from here we obtain, using Eqn. (3.2): $$\langle(v_\alpha-u_\alpha)(v_\beta-u_\beta)\rangle=\delta_{\alpha\beta}u^2_S\int_1^\infty\frac{\d x}
{x(1+\frac{2\tau_S}{\tau_L}x^\frac{1}{3})}
\underset{\scriptscriptstyle \tau_S\ll\tau_L}\longrightarrow 
3\delta_{\alpha\beta}u^2_S\log(\tau_L/\tau_S)
\eqno(4.5)$$ where $$u_S=\Big(\frac{\tau_S}{3\tau_L}\Big)^\frac{1}{2}u_T
\eqno(4.6)$$ for $\tau_S<\tau_L$, is the velocity scale of eddies with lifetime $\tau_S$ and $u_T$ is the turbulent velocity defined in Eqn. (3.3). In order to proceed to next order, it is necessary to calculate the trajectory separation: $$\z^\smalP(t|\x,0)-\z(t|\x,0)=\u_Gt+(1-\ex^{-t/\tau_S})
\int_{-\infty}^0\d\tau\ \ex^{\tau/\tau_S}\u^\smalL(\x,\tau)$$ $$-\int_0^t\d\tau\exp(-\frac{t-\tau}{\tau_S})\u^\smalL(\x,\tau)
\eqno(4.7)$$ We notice from this equation that the inertia produced part of trajectory separation does not grow indefinitely. In other words, if $\u_G=0$ and to lowest order in $\rho^{-1}$, there will be localization of solid particle trajectories around the 