Dynamics of inertial particles in two-dimensional planar flow have been investigated by evaluating finite-time Lyapunov exponents (FTLE). The first part of our work deals with inertial particle dynamics. The Maxey-Riley equations have been employed to track particles. Patterns formed by inertial particles are reported along with their dependance on Strokes number and density of particles relative to the carrier-fluid density. Our results distinguish patterns formed by particles denser than the fluid (aerosols) from those formed by particles lighter than the fluid (bubbles). Preferential concentration of these particles at specific regions of the flow have been observed. The attenuating, low-pass filter effect of Stokes drag on bubbles are reported for the first time. The results from this part of the work motivated further investigations into the underlying organizing structures of the flow, namely the Lagrangian coherent structures (LCS). LCS is traditionally evaluated using FTLE. In the next part of the work, our objective was to interpret the dynamics of inertial particles by evaluating finite-time Lyapunov exponents on their trajectories. A main result is that aerosols were found to be attracted and preferentially concentrated along ridges of negative finite-time Lyapunov exponents (nFTLE) of the underlying flow. On the other hand bubbles were found to be repelled from these structures and were therefore observed preferentially concentrating away from these zones. These results, being reported for the first time, supplement the existing literature on preferential concentration of inertial particles. Despite having an effect on particle trajectories, increasing the Stokes number had very little effect on inertial finite-time Lyapunov exponents (iFTLE). Furthermore, increasing Stokes number resulted in an increase in the ridges of iFTLE contours for aerosols, whereas for bubbles the opposite was observed. These findings indicate that optimum mixing occurs at different Stokes numbers for aerosols and bubbles. The last part of the work focused on comparing well-known dispersion measures with inertial finite-time Lyapunov exponents. We qualitatively show that two-point dispersion contours share dominant ridges with those from inertial finite-time Lyapunov exponents. This result numerically shows that material surfaces identified by inertial finite-time Lyapunov exponents are maximally dispersed in the flow. Applications and future directions based on our work are suggested.

This is targeted at professionals and graduate students working in disciplines where flow of adhesive particles plays a significant role.

In this work, we examine the motion of particles which are subjected to varying levels of turbulence, inertia, and gravity, in both homogeneous and inhomogeneous turbulence. These investigations are performed through direct numerical simulation (DNS) of the Eulerian fluid velocity field combined with Lagrangian particle tracking. The primary motivation of these investigations is to better understand and model the dynamics and growth of water droplets in warm, cumulus clouds. In the first part of this work, we discuss the code we developed for these simulations, Highly Parallel Particle-laden flow Solver for Turbulence Research (HiPPSTR). HiPPSTR uses efficient parallelization strategies, timeintegration techniques, and interpolation methods to enable massively parallel simulations of three-dimensional, particle-laden turbulence. In the second, third, and fourth sections of this work, we analyze simulations of particle-laden flows which are representative of those at the edges and cores of clouds. In the second section, we consider the mixing of droplets near interfaces with varying turbulence intensities and gravitational orientations, to provide insight into the dynamics near cloud edges. The simulations are parameterized to match windtunnel experiments of particle mixing which were conducted at Cornell, and the DNS and experimental results are compared and contrasted. Mixing is suppressed when turbulence intensities differ across the interface, and in all cases, the particle concentrations are subject to large fluctuations. In the third and fourth sections, we use HiPPSTR to analyze droplet motion in isotropic turbulence, which we take to be representative of adiabatic cloud cores. The third section examines the Reynolds-number scaling of single-particle and particle-pair statistics without gravity, while the fourth section shows results when gravity is included. While weakly inertial particles preferentially sample certain regions of the flow, gravity reduces the degree of preferential sampling by limiting the time particles can spend interacting the underlying turbulence. We find that when particle inertia is small, the particle relative velocities and radial distribution functions (RDFs) are almost entirely insensitive to the flow Reynolds number, both with and without gravity. The relative velocities and RDFs for larger particles tend to weakly depend on the Reynolds number and to strongly depend on the degree of gravity. While non-local, path-history interactions significantly affect the relative velocities of moderate and large particles without gravity, these interactions are suppressed by gravity, reducing the relative velocities. We provide a physical explanation for the trends in the relative velocities with Reynolds number and gravity, and use the model of [198] to understand and predict how the trends in the relative velocities will affect the RDFs. The collision kernels for particles representative of those in atmospheric clouds are generally seen to be independent of Reynolds number, both with and without gravity, indicating relatively low Reynolds-number simulations are able to capture much of the physics responsible for droplet collisions in clouds. We conclude by discussing practical implications of this work for the cloud physics and turbulence communities and suggesting areas for future research.