Effect of gravity on clustering patterns and inertial particle attractors in kinematic simulations

In this paper, we study the clustering of inertial particles using a periodic kinematic simulation. The systematic Lagrangian tracking of particles makes it possible to identify the particles' clustering patterns for different values of particle inertia and drift velocity. The different cases are characterized by different pairs of Stokes number (St) and Froude number (Fr). For the present study, $0\le \mathrm{St}\le 1$ and $0.4\le \mathrm{Fr}\le 1.4$. The main focus is to identify and then quantify the clustering attractor—when it exists—that is the set of points in the physical space where the particles settle when time goes to infinity. Depending on the gravity effect and inertia values, the Lagrangian attractor can have different dimensions, varying from the initial three-dimensional space to two-dimensional layers and one-dimensional attractors that can be shifted from a horizontal to a vertical position.