= Richardson pair dispersion
{c}
{title2=$\langle r^2(t)\rangle\sim g\epsilon t^3$}
= Richardson dispersion
{c}
{synonym}
Richardson pair dispersion concerns relative separation of two marked <fluid elements>, rather than their centre-of-mass motion. In an <inertial range>, scale-local relative diffusivity is of order $\epsilon^{1/3}r^{4/3}$. A self-similar closure gives $d\langle r^2\rangle/dt=A\epsilon^{1/3}\langle r^2\rangle^{2/3}$ and hence a $t^3$ regime after loss of memory of initial separation. Stationarity and inertial-range separation alone do not imply this law at arbitrarily short times.
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