Generalization of Turbulent Pair Dispersion to Large Initial Separations

TL;DR

This paper extends the understanding of turbulent pair dispersion to larger initial separations by introducing a new time scale, demonstrating that certain pairs follow Richardson's superdiffusive regime and exhibit specific scaling behaviors.

Contribution

It introduces a new time scale, $ au_{v_0}$, to generalize turbulent pair dispersion for large initial separations, supported by experimental evidence.

Findings

Pairs with shorter $ au_{v_0}$ separate in the Richardson regime.

Delay times scale as $ ho^{2/5}$ for these pairs.

The new scale captures persistence of initial conditions.

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.