Generalization of Turbulent Pair Dispersion to Large Initial Separations

Abstract: We present a generalization of turbulent pair dispersion to large initial separations ($\eta < r_0 < L$), by introducing a new time scale, $\tau_{v_0}$, that reflects the persistence of initial conditions at time $\tau=0$. Results of 3D Lagrangian tracking experiments at moderate Reynolds numbers show that pairs, for which the new time scale is shorter than the eddy turnover time scale, separate as in the Richardson superdiffusive regime, $\langle \Delta r^2 \rangle \propto \tau^3$. The analysis of delay times (time interval to cross $\Delta r = \rho \, r_0$) of these conditionally sampled pairs exhibit $\rho^{2/5}$ scaling.