Relative Dispersion of Ice Crystals in Seeded Cumuli

Abstract

Relative dispersion of ice crystals was measured in 30 seeded cumulus clouds. A quasi-instantaneous, vertical area source of ice was generated by releasing dry-ice pellets from an airplane. The ice concentration distribution and relative dispersion were measured normal to the source and were complemented by cloud turbulence measurements, namely, velocity variances and the energy dissipation rate ?. The clouds were selected based on an objective set of criteria and were treated as members of the same ensemble. The observed mean relative dispersion σrx agreed well with predictions from a Lagrangian stochastic two-particle model, which reproduces Batchelor's theoretical results for σrx. For short times t after the seeding time ts, the predictions and observations suggested a growth like σrx ? t ? ts rather than Batchelor's ?intermediate? time prediction, σrx ? ?1/2 (t ? ts)3/2. This difference was attributed to the rather large initial dispersion σ0 of ice crystals, 27?53 m, inferred from the measurements; Batchelor's result is only valid for σ0 ? σva3/?, where σva2 is the average velocity variance. At long times, the predictions and observations approached the same asymptotic limit, σrx ? (t ? ts)1/2. In addition to the mean dispersion, probability density functions (pdfs) of the individual dispersion observations were constructed and showed an evolution from a highly skewed pdf at small times to a more symmetrical one at large times. This is one of the first reports of the σrx pdf, which is important for determining the variance and pdf of the randomly varying concentration in a small ice cloud or plume of material.