To help better explain the gap between theoretical and observed precipitation droplet growth times, Xue et al. attempted to quantify the effects of turbulent motions on collision and coalescence. In “Growth of Cloud Droplets by Turbulent Collision-Coalescence” from the February 2008 Journal of the Atmospheric Sciences, several different model parameterizations for collision kernels were compared in attempt to more accurately portray the time span of droplet growth. Prior to this study, numerous attempts had been made to overcome this deficiency. At first, most used a qualitative approach. When others tried a quantitative approach, they failed to take into account things such as the gravitational force in addition to turbulence, and fell short.
The comparison of the parameterizations for the five different turbulent collision kernels revealed their strengths and weaknesses. A general kinematic formulation, radial distribution function (RDF), gravitational force, Stokes drag force (related to terminal velocity), and other effects were combined in different ways and used in model outputs. The Ayala or A05 kernel turned out to be the most realistic. The resulting kernels were evaluated through plots of kernel size as determined by collision droplet size. They were also compared with the Hall kernel (a base kernel commonly used in collision-coalescence that does not take turbulence into account) to measure the enhancement effects of turbulence in each parameterization. Moderate enhancement was seen in the Ayala kernel, the ZWW-RW overestimated the enhancement, and the remaining two were similar to that of the Hall kernel.
For the remainder of the paper, the Ayala kernel is understood to be the most realistic, so I will include the effects for only that kernel, unless another proves to be more relevant. In turbulence enriched collision and coalescence, size matters. Droplets were arranged into three classifications (A,B, and C) depending on their size. Group A included drops of radius < 50µm, B was between 50 and 100µm, and C was drops > 100µm. The Ayala kernel showed maximum turbulence effects at small and medium sized droplets colliding with droplets of similar size. This illustrates the concept of the preferential concentration of droplets, an idea closely related to the enhancement of collisions through turbulence.
When looking at the temporal aspect of droplet growth, three phases were identified: the autoconversion phase, accretion phase, and the self-collection phase. All three phases can be fairly easily identified on plots of mass density transfer. The radii for the maxima on the graphs can then be translated into radii verses time graph. Maximum droplet growth occurs during the accretion phase. Turbulence helps to initiate the onset of phase two faster, and therefore increases the likelihood of larger drops. From this, they found that the Ayala kernel can shorten the time for drizzle drop formation by up to 39% compared to the Hall kernel.
While the math and numerical simulations involved in this paper may be beyond my realm of understanding, the concepts and ideas presented seemed relevant. The individual steps to reach their conclusions were somewhat confusing, but the conclusions made perfect sense. In my mind I compared it somewhat to an updraft increasing the final droplet size. Turbulence increases the opportunity for more collisions and therefore decreases the time it takes to create precipitation sized droplets.