 Richardson pair dispersion

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 ${ϵ}^{1/3}{r}^{4/3}$. A self-similar closure gives $d⟨r^2⟩/dt=A{ϵ}^{1/3}⟨r^2{⟩}^{2/3}$ 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.