Fine-Scale Droplet Clustering in Atmospheric Clouds: 3D Radial Distribution Function from Airborne Digital Holography

Abstract

The extent of droplet clustering in turbulent clouds has remained largely unquantified, and yet is of possible relevance to precipitation formation and radiative transfer. To that end, data gathered by an airborne holographic instrument are used to explore the three-dimensional spatial statistics of cloud droplet positions in homogeneous stratiform boundary-layer clouds. The three-dimensional radial distribution functions g(r) reveal unambiguous evidence of droplet clustering. Three key theoretical predictions are observed: existence of positive correlations, onset of correlation in the turbulence dissipation range, and monotonic increase of g(r) with decreasing r. This implies that current theory captures the essential processes contributing to clustering, even at large Reynolds numbers typical of the atmosphere.

Pitfalls Measuring 1D Inertial Particle Clustering

“…Turbulent flows laden with inertial particles constitute an active research area within multiphase fluid mechanics due to their potential applications in fields such as planetary formation, pollutant modeling, and cloud formation [3,4]. Several methods are available to characterize particle-clusters, with Voronoï-tessellation [5,6,7,8] becoming increasingly popular in both experimental studies employing visualization techniques, e.g., Particle Tracking Velocimetry (PTV) [2,9] and numerical simulations.…”

A model study of the effect of clustering on the last stage of drizzle formation

“…Nevertheless the magnitude of the instantaneous pair-correlation function at short distances from the collector drop must be nearly what it sees over that distance of fall. Larsen et al (2018) found that at a distance of 1 mm the magnitude of the pair correlation function is ∼10 −2 , for clouds with dissipation rates ∼10 −4 − 10 −3 m 2 ⋅s −3 . For shorter distances still we must rely on estimates from numerical studies based on simple model flows characterized by relatively low Reynolds number.…”

“…For the 40 µm collector drop U ≈ 0.3 m·s −1 (Rogers and Yau, ) and for cumulus clouds ε ≤ 10 −1 m 2 ·s −3 (Grabowski and Wang, ), hence L could be of the order of a metre as per our crude scaling argument. However, this is likely an overestimate, since the most intense clustering is found to be at the dissipation scales, as revealed also by the recent in‐cloud measurements (Larsen et al ., ). Hence L cannot be far from the dissipation scale of the in‐cloud turbulence.…”

“…Larsen et al . () found that at a distance of 1 mm the magnitude of the pair correlation function is ∼10 −2 , for clouds with dissipation rates ∼10 −4 − 10 −3 m 2 ·s −3 . For shorter distances still we must rely on estimates from numerical studies based on simple model flows characterized by relatively low Reynolds number.…”

“…Although these studies utilized idealized flows (homogeneous, isotropic turbulence or synthetic random flows) and were limited to lower Reynolds numbers compared to the clouds, one hopes that the results will carry over to actual clouds and therefore that the clustering must be a major cause of rapid cloud-droplet growth. Further, measurements have ascertained that the cloud droplets are indeed clustered (Jameson and Kostinski, 2000;Kostinski and Shaw, 2001;Kostinski and Jameson, 2003;Pinsky and Khain, 2003;Lehmann et al, 2007;Larsen et al, 2018).…”