Lagrangian coherent structures and the dynamics of inertial particles

In this work we investigate the dynamics of inertial particles using the finite-time Lyapunov exponent (FTLE). In particular, we analyze preferential concentration of particles with nonzero Stokes number, $St$, and varying density ratio, $R$, for the double gyre vector field. We find that heavy particles (aerosols) tend to accumulate strongly onto negative-time (attracting) FTLE ridges of the non-inertial fluid particles, while lighter particles (bubbles) tend to repel from these ridges and accumulate at vortex cores. The transition of the negative-time FTLE ridges from attractors to repellers, based on the value of $R$, partially explains the preferential concentration of inertial particles. We also investigate the inertial finite-time Lyapunov exponent (iFTLE) based on the trajectories of inertial particles. The iFTLE is used to quantify the effect of $St$ and $R$ on particle stirring, and we present preliminary results establishing a connection between iFTLE and the two-point dispersion. Finally, we analyze the low-pass filtering effect of Stokes number on particle trajectories.