The tools used by the organizations in charge of predicting the air quality are designed to estimate average fields and do not quantify the amplitude of fluctuations. The neighborhood impact of sources of air toxics is generally evaluated using a combination of Gaussian models for dispersion and of half-empirical techniques. However, in some situations, unwanted local concentrations presenting health hazards win over turbulent diffusion. Quantifying fluctuations to identify situations where mean-field approaches fail is hence an important and challenging issue.
The goal is here to give a precise and systematic description of three general mechanisms that have been identified as provoking large fluctuations of concentration.
Nature of the turbulent flow
It was observed that the distribution of a passive scalar advected by a turbulent flow displays tails that are much fatter than Gaussian. However the functional form of such tails does not seem universal but could depend on the flow details (mean shear, isotropy, homogeneity, etc.). The goal will be here to identify the flow characteristics favoring or impeding extreme concentrations.
Some pollutants are so massive that size and mass effects play an important role in their dynamics. It is for instance the case of particles labeled as PM2.5 and PM10, which are mostly coming from the combustion of petroleum products and can have important effects on health. Such particles are typically ejected from the eddies of the turbulent flow and concentrate in strain-dominated regions; this results in a broadening of the probability tails at large concentrations. It is proposed to quantify the importance of such inertial mechanisms as a function of the nature of the particles.
Nature of the source
The downwind concentration of pollutants is markedly affected by the injection details. A description of the particle spatial distribution requires determining the amalgam between plum growth driven by turbulent eddies smaller than the puff and dispersion caused by meandering. The respective weight of these two effects is sensitive to source parameters such as its size and its spatial extent (point-like to caricature a stack, extended in one direction to mimic a road, or in two for forest fires or dust storms), its time behavior (instantaneous or continuous), or its distance to the ground. It is intended here to develop new tools that will provide a unified description of cases that, up to now, were mostly described in specific settings.
Clouds are formed by the condensation of water vapor onto nuclei in a rising mass of moist air. This produces droplets with sizes of the order of several microns. To precipitate, such droplets have to grow to millimeter sizes, either by coagulating together or by freezing and capturing the water evaporating from super-cooled droplets (Bergeron process). Air turbulence might strongly affect these fundamental microphysical mechanisms, whose understanding is crucial for determining the cloud droplet size distribution and the timescales of rain activation. Their accurate modeling as a function of the dynamical properties of the cloud represents a formidable challenge.
The proposed work aims at providing a detailed knowledge of the influence of turbulence on these processes and more particularly of the contribution of strong fluctuations to their overall contribution.
Condensation and evaporation
The idea is to quantify the turbulence-induced broadening of the droplet-size distribution at the initial stage of cloud formation. Recent work either focuses on the role of entrainment/mixing of dry air inside the cloud or uses stochastic condensation techniques based on turbulent closures. The idea is to develop analytically tractable models that unify both approaches. One of the objectives will be to describe the mechanisms responsible for the presence in clouds of droplets with radii much larger than the maximal size predicted by the models where isolated rising volumes of cloud are considered. Such “super-adiabatic” droplets have experienced violent fluctuations of the super-saturation field along their path. Their description requires thus detailing the intermittent spatial jumps associated to extremely sharp gradients of the water vapor content.
Coalescence of droplets in warm clouds
Two mechanisms have been recently identified as intensifying collisions between droplets: the presence of large concentration fluctuations and the formation of caustics (also referred to as the “sling effect”), enhancing velocity differences between close particles. A first objective is to quantify these effects for polydisperse droplets and as a function of the flow dynamical properties (statistics of large accelerations, Reynolds number, anisotropies and inhomogeneities). These effects can be implemented in effective collision kernels that are used in kinetic models (Smoluchowsky equation). A second objective is here to determine the limits of validity of such mean-field approaches by identifying and controlling the fluctuations responsible for local strong deviations from the average.
Formation of crystals
Ice nucleation and crystal growth are currently modeled using standard turbulence closures. Understanding the detailed microphysics of these processes in a fluctuating turbulent environment is still an open problem. The growth of crystals implies both deposition of water vapor and aggregation. Based on the two previous points, it is proposed to give a better knowledge of the influence of turbulence on the balance between these two physical mechanisms.