LAUSR

Abstract The formation and life-span of clouds as well as the associated unsteady processes concerning the micro-physics of the water phases they may contain are open questions in atmospheric physics. We here use three-dimensional direct numerical simulation to analyse the temporal evolution of a small portion of the top of a cloud. The Eulerian description of the turbulent velocity, temperature and vapor fields is combined with the Lagrangian description of two different ensembles of cloud droplets, that is, with a monodisperse and a polydisperse size distribution. A shear-free turbulent mixing layer is used to model the background air flow of the cloud top. This flow is considered appropriate because clouds cannot stand the presence of shear, which inevitably destroys them quickly. Luke-warm clouds are generally found at an altitude of 1000-2000 meters, live for a few hours or up to 1-2 days, continuously change shape, and have typical dimensions of some hundreds of meters. The global time-scale of these changes is recognized as being of the order of 100 seconds ( Shaw (2003) , Warhaft (2009) ). From the formation phase to the dying out phase, clouds live under a continuous sequence of transients that are slightly different one from the other. In this study, we have tried to reduce the simplification level with respect to the real warm cloud situation as much as possible. We have included the same level of supersaturation of warm clouds, the same amount of liquid water content, and thus, the same numerical number of water droplets, and finally, a typical unstable perturbation of the density stratification and a typical kinetic energy cloud / clear air ratio (order of 10). We have considered an observation duration of the order of a few seconds (about 10 initial turnaround times). During this time, the kinetic energy decays throughout the system by 95%. It should be recalled that the kinetic energy inside the interfacial layer (the shear-free turbulent mixing layer that matches the cloud region to the ambient air region) also decays spatially, by nearly 85%. We observed, with respect to the cloud region, in the interfacial layer, a five times faster achievement of a common value of standard deviation for the probability density of both the monodisperse and poly-disperse populations. This acceleration of the dynamics is remarkable and is somewhat counterintuitive. It is closely correlated with the intermittency of the small scale of the air flow and of the supersaturation fluctuation. We give information on the size distribution of both the positive and negative droplet growth and on the drop size and the corresponding numerical concentration value of the distribution peak as time passes. Finally, we comment on the extension of the concept of the collision kernel for an unstable and inhomogeneous system in which turbulence decays faster than the time scales of the involved aqueous phases.