Preferred Location of Droplet Collisions in Turbulent Flows

In cloud physics, droplets and the way they collide, are at the very base of the formation of clouds and the initiation of warm rain. This stage in which droplet growth is dominated by collision and coalescence occurs after the condensation stage, in which condensation is the leading process. The third and last stage of rain formation is the sedimentating stage in which gravity plays a crucial role (e.g. Shaw (2003)).

The idea about in-cloud droplet dynamics is that turbulence may significantly increase the collision probability and therefore accelerate rain formation (Shaw, 2003; Jonas, 1996; Grabowski and Wang, 2013). Turbulent fluctuations in a flow lead to continuously varying drag forces on a droplet, which leads to large variations in droplet velocities and more collisions (Pinsky and Khain, 1997). Turbulence also tends to cluster droplets at the smallest scale in regions of low enstrophy, a process called preferential concentration(Squires and Eaton, 1991).

This study investigates the local flow characteristics near droplet-droplet collisions by means of Direct Numerical Simulation (DNS) of isotropic cloud-like turbulence. The key finding is that, generally, droplets do not collide where they preferentially concentrate. Preferential concentration is found to happen as expected in regions of low enstrophy (vorticity magnitude), but collisions tend to take place in regions with significantly higher dissipation rates (up to a factor of 2.5 for Stokes unity droplets). Investigation of the droplet history reveals that collisions are consistently preceded by dissipative events. Based on the droplet history data, the following physical picture of a collision can be constructed: enstrophy makes droplets preferentially concentrate in quiescent flow regions, thereby increasing the droplet velocity coherence, i.e. decreasing relative velocities between droplets. Strongly clustered droplets thus have a low collision probability, until a dissipative event accelerates the droplets towards each other. Finally we study the relation between the local dissipation rate and the local collision kernel and vary the averaging scale to relate the results to the globally averaged collision and dissipation rates. It is noted that, unlike enstrophy, there is a positive correlation between the dissipation rate and collision efficiency that extends from the largest to the smallest scales of the flow. Inside a Large Eddy Simulation framework, this knowledge can for example be used to investigate the effect intermittency has on the cloud droplets growth and rain initiation time.

Wojciech W. Grabowski and Lian-Ping Wang. Growth of cloud droplets in a turbulent environment. Annual Review of Fluid Mechanics, 45(1):293–324, 2013.

P.R. Jonas. Turbulence and cloud microphysics. Atmospheric Research, 40:283–306, May 1996.

M. B. Pinsky and A. P. Khain. Turbulence effects on the collision kernel.I: formation of velocity deviations of drops falling within a turbulent three-dimensional flow. Quarterly Journal of the Royal Meteorological Society, 123(542):1517–1542, July 1997.

Raymond A. Shaw. Particle-turbulence interaction in atmospheric clouds.Annu. Rev. Fluid Mech., 35(1):183–227, January 2003.

K. D. Squires and J. K. Eaton. Preferential concentration of particles by turbulence. Physics of Fluids A-fluid Dynamics, 3(5):1169–1179, May 1991.