Lagrangian tracking simulation of droplet growth in turbulence-turbulence enhancement of autoconversion rate

The authors describe the Lagrangian cloud simulator (LCS), which simulates droplet growth in air turbulence. The LCS adopts the Euler-Lagrangian framework and can provide reference data for cloud microphysical models by tracking the growth of particles individually. The collisional growth in a stagnant flow is calculated by the LCS and also by solving the stochastic collision-coalescence equation (SCE). Good agreement is obtained between the LCS and SCE simulations. Comparisons between the results for stagnant and turbulent flows confirm that in-cloud turbulence enhances collisional growth. The enhancement is well predicted by the SCE method if a proper collision model is employed. To quantify the enhancement, the paper defines the time scale of the autoconversion process, in which cloud droplets grow into raindrops through collisions, as the time taken for 10% of the cloud to become rain (t10%). The authors then define the turbulence enhancement factor E_turb as, where the overbar denotes the mean value of the LCS runs and the subscripts NoT and T indicate stagnant (nonturbulent) flow and turbulent flow simulations, respectively. It was found that the enhancement factor increases linearly with the energy dissipation rate, while it does not show a consistent dependence on the Reynolds number. The levels of statistical fluctuations in the autoconversion time scales were directly obtained for the first time. It is shown that the relative standard deviation of t10% simply follows the power law that the binomial distribution theory predicts, independently of the flow conditions.