= Diffusive large-scale pair dispersion
{title2=$\mathbb E|\boldsymbol l(t)|^2\sim 2t\int_0^\infty R_{\mathrm{rel}}(s)ds$}
At separations well above the <integral scale of turbulence>, two fluid velocities can decorrelate spatially. If the relative-velocity <autocorrelation> $R_{\mathrm{rel}}$ is stationary and integrable, the displacement identity used in <Taylor turbulent dispersion> gives the displayed long-time linear mean-square growth. With speed $U$ and <Lagrangian integral time> of order $L/U$, its relative <diffusivity> is of order $UL$. The characteristic separation grows as $t^{1/2}$, unlike inertial-range <Richardson pair dispersion>.
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