Statistical model for collisions and recollisions of inertial particles in mixing flows

Transport of condensing droplets in Taylor-Green vortex flow in the presence of thermal noise

We study the role of phase change and thermal noise in particle transport in turbulent flows. We employ a toy model to extract the main physics: Condensing droplets are modelled as heavy particles which grow in size, the ambient flow is modelled as a two-dimensional Taylor-Green flow consisting of an array of vortices delineated by separatrices, and thermal noise are modelled as uncorrelated Gaussian white noise. In general, heavy inertial particles are centrifuged out of regions of high vorticity and into regions of high strain. In cellular flows, we find, in agreement with earlier results, that droplets with Stokes numbers smaller than a critical value, St<St_{cr}, remain trapped in the vortices in which they are initialized, while larger droplets move ballistically away from their initial positions by crossing separatrices. We independently vary the Péclet number Pe characterizing the amplitude of thermal noise and the condensation rate Π to study their effects on the critical Stokes number for droplet trapping, as well as on the final states of motion of the droplets. We find that the imposition of thermal noise, or of a finite condensation rate, allows droplets of St<St_{cr} to leave their initial vortices. We find that the effects of thermal noise become negligible for growing droplets and that growing droplets achieve ballistic motion when their Stokes numbers become O(1). We also find an intermediate regime prior to attaining the ballistic state, in which droplets move diffusively away from their initial vortices in the presence of thermal noise.

Fine-Scale Droplet Clustering in Atmospheric Clouds: 3D Radial Distribution Function from Airborne Digital Holography

The extent of droplet clustering in turbulent clouds has remained largely unquantified, and yet is of possible relevance to precipitation formation and radiative transfer. To that end, data gathered by an airborne holographic instrument are used to explore the three-dimensional spatial statistics of cloud droplet positions in homogeneous stratiform boundary-layer clouds. The three-dimensional radial distribution functions g(r) reveal unambiguous evidence of droplet clustering. Three key theoretical predictions are observed: the existence of positive correlations, onset of correlation in the turbulence dissipation range, and monotonic increase of g(r) with decreasing r. This implies that current theory captures the essential processes contributing to clustering, even at large Reynolds numbers typical of the atmosphere.

Enhanced droplet collision rates and impact velocities in turbulent flows: The effect of poly-dispersity and transient phases

We compare the collision rates and the typical collisional velocities amongst droplets of different sizes in a poly-disperse suspension advected by two- and three-dimensional turbulent flows. We show that the collision rate is enhanced in the transient phase for droplets for which the size-ratios between the colliding pairs is large as well as obtain precise theoretical estimates of the dependence of the impact velocity of particles-pairs on their relative sizes. These analytical results are validated against data from our direct numerical simulations. Our results suggest that an explanation of the rapid growth of droplets, e.g., in warm clouds, may well lie in the dynamics of particles in transient phases where increased collision rates between large and small particles could result in runaway process. Our results are also important to model coalescence or fragmentation (depending on the impact velocities) and will be crucial, for example, in obtaining precise coalescence kernels in such systems.