Fig. 3: Evolution of the pair dispersion angle.
a Evolution of the average angle between the separation and the relative velocity vectors as a function of time. Continuous lines show DNS results for various ensembles grouped by the initial separation distance for values in the inertial range; the bin edges used to form the ensembles are l0/η = 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 130, 160, and 200, where the arrow runs from lower to higher values. Lines in the inset show the same data plotted with time normalized by the Batchelor timescale. Circles correspond to the experimental results, averaged over all pairs with r0 < 70η with an uncertainty of ± 2∘ based on the data range across the l0 groups (Fig. S3). The dot-dashed line correspond to eq. (9). The dashed black line and the shaded region mark the estimated value of \(\left\langle \theta \right\rangle=59.3\pm {2}^{\circ }\). b Evolution of the average of θ for pairs with initial separation outside the inertial range. Data are shown for initial separation distances of l0/η = 483, 594, 704, 812, 915, and 1006. These values correspond to l0/L = 1.00, 1.24, 1.47, 1.69, 1.91, and 2.10. The horizontal dashed line marks the \(\left\langle \theta \right\rangle=59.{3}^{\circ }\) value, and the vertical dashed line marks one integral timescale.
