Lagrangian coherent structures and the dynamics of inertial particles
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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 focussed 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.
- Applied mathematics