Investigation of Turbulent Entrainment-Mixing Processes with a New Particle-Resolved Direct Numerical Simulation Model

13 A new particle-resolved three dimensional direct numerical simulation (DNS) model is 14 developed that combines Lagrangian droplet tracking with the Eulerian field representa15 tion of turbulence near the Kolmogorov microscale. Six numerical experiments are per16 formed to investigate the processes of entrainment of clear air and subsequent mixing with 17 cloudy air and their interactions with cloud microphysics. The experiments are designed 18 to represent different combinations of three configurations of initial cloudy area and two 19 turbulence modes (decaying and forced turbulence). Five existing measures of microphys20 ical homogeneous mixing degree are examined, modified, and compared in terms of their 21 ability as a unifying measure to represent the effect of various entrainment-mixing mecha22 nisms on cloud microphysics. Also examined and compared are the conventional Damköh23 ler number and transition scale number as a dynamical measure of different mixing mech24 anisms. Relationships between the various microphysical measures and dynamical mea25 sures are investigated in search for a unified parameterization of entrainment-mixing pro26 cesses. The results show that even with the same cloud water fraction, the thermodynamic 27 and microphysical properties are different, especially for the decaying cases. Further anal28 ysis confirms that despite the detailed differences in cloud properties among the six sim29 ulation scenarios, the variety of turbulent entrainment-mixing mechanisms can be reason30 ably represented with power-law relationships between the microphysical homogeneous 31 mixing degrees and the dynamical measures. 32