In this thesis, the correlation between mixing and entrainment/detrainment at the cloud edge, and the dynamics of particles/droplets is investigated. At the edge of a cloud, entrainment of unsaturated environmental air plays a very crucial role. Evaporation of cloud droplets exposed to unsaturated air results in the formation of a negatively buoyant layer, commonly referred to as the subsiding shell in literature.
A systematic study of the dynamics of the subsiding shell using direct numerical simulations demonstrates the self-similar characteristics of the flow in the shell. A canonical setup is developed whereby a developing temporal plume is used as a paradigm for a small portion of the edge of a cloud. Characteristic scales for the shell thickness, buoyancy and velocities are identified using integral relations from \textcite{Ref24}. Results reveal a buoyancy driven shell with the in-shell mean velocity being passive and slaved to the buoyancy.
Different interfaces are identified at the cloud edge as a result of the generation of the subsiding shell. This includes a Turbulent-Non Turbulent Interface (TNTI) which is detected by applying thresholds on the enstrophy. Lagrangian particles crossing the TNTI exhibit sharp jumps in enstrophy and buoyancy when compared to traditional cloud boundaries which are shown to be dynamically unimportant.

A study of the effect of gravity on clustering in a polydisperse distribution of droplets in isotropic homogeneous decaying turbulence is performed. The radial distribution function is used to quantify clustering and analysis reveals that gravity suppresses clustering in sedimenting droplets due to reduced droplet-turbulence interaction times. Comparisons are also made with analytical and empirical relations and very good agreement is observed.

Different aerosol concentrations (clean and polluted clouds) are simulated by varying the initial size distribution of droplets, and the resulting effect of entrainment on the droplet size distributions and shell strength is investigated. Simulations reveal a dynamical positive feedback where droplet evaporation increases the turbulent kinetic energy which further drives entrainment and evaporative cooling. The droplet size distribution is found to be broader for initial size distributions with a larger mean droplet radius but smaller particle concentrations (clean clouds).