Clouds are the largest source of uncertainty in climate prediction models. Their properties depend on delicate mechanical and thermodynamic interactions between air, water vapor, droplets and the heat and radiative transfers between these different phases. The wide ranges of scale involved and the complexity of these processes are such that until now, the clouds remained largely inaccessible, both by the most advanced numerical simulations and by the most sophisticated experimental devices. Also, accessing their fine properties in situ by instrumented platforms is still a real challenge.
Estimating binary collision rates in cloud coalescence processes requires knowing the flux at which droplets approach each other. A notable effect is that the velocity differences between very close particles can be arbitrarily large. This is linked to the presence of caustics in the distribution of particles: several droplets with very different speeds can be simultneously present at the same location. This effect is not present for the tracers and increasingly dominates the dynamics when inertia increases. From a statistical point of view, the signature of such caustics is an effective Hölder exponent for the droplet velocity field that is different from that of the fluid. This exponent tends towards one in the zero inertia limit and towards zero with very large Stokes numbers.
The most significant influence of turbulence on the gravitational settling of droplet is the increase in their terminal velocity due to a preferential sampling of the regions of flow where the vertical velocity points downwards. This effect can be quantified as a function of the turbulence level of the airflow (Reynolds and Froude number) and the size of the droplets (Stokes number). Gravitational settling is also responsible for a bi-dimensionalization of the dynamics in the horizontal directions.
The population dynamics of cloud droplets is usually described in terms of Smoluchowski's coagulation kinetics. This approach fails when the coalescing species are dilute and transported by a turbulent flow. The intermittent Lagrangian motion involves correlated violent events that lead to an unexpected rapid occurrence of the largest particles. This new phenomena can be quantified in terms of the anomalous scaling of turbulent three-point motion, leading to significant corrections in macroscopic processes that are critically sensitive to the early-stage emergence of large embryonic aggregates in rain precipitation.
Using direct numerical simulations, one can show that turbulent fluctuations in the super-saturation field can provide different conditions for droplet growth. These conditions change in time and space following turbulent transport and mixing. Based on these observations, one can design a stochastic Lagrangian consisting of a set of integral-differential stochastic equations describing the joint evolution of the square radius of the droplets and the super-saturation field along their trajectory. The model depends on two dimensionless parameters that account for the total amount of water (liquid + vapor), the cloud thermodynamic properties and the turbulent Lagrangian integral time of the turbulent super-saturation field. Depending on these parameters, different steady size distributions are obtained.