High-resolution hybrid direct numerical simulation of turbulent collision of cloud droplets

Clouds play an essential role in the weather, the hydrological cycle, and the earth's climate system. Turbulent collision-coalescence of cloud droplets governs the conversion of cloud droplets to rain drops. Accurate parameterization of turbulent collision of cloud droplets requires a first-principle based theoretical tool that can accurately represent droplet-droplet and droplet-turbulence interactions. In recent years, we have developed a hybrid direct numerical simulation (HDNS) approach to quantify geometric collision rate, collision efficiency, and related kinematic pair statistics that are needed to parameterize the turbulent collision kernel. The HDNS data have guided the development of our first version of the turbulent collision kernel. Previous HDNS simulations were typically performed on $128^3$ grid with a small volume [~(20 cm)$^3$] and low flow Reynolds numbers, thus not all droplet-turbulent airflow interactions can be considered.

To extend our previous HDNS data and theoretical parameterization, here we report on new results obtained using $256^3$ and $512^3$ grid resolutions. These resolutions cover a larger domain, allowing a wider range of small-scale turbulence scales to be included. In order to perform such simulations, domain-decomposition based MPI implementations are employed to make it possible to run our HDNS code on a larger number of parallel processors. We shall first review several implementation and validation issues. We then investigate both dynamic and kinematic collision statistics for different droplet sizes, flow dissipation rates, and flow Reynolds numbers, including the dynamic collision rate, radial relative velocity, and radial distribution function. Implications of these high-resolution results to the parameterization of turbulent collision kernel and its application in dynamic cloud models will also be discussed.