# Effect of energy spectrum law on clustering patterns for inertial particles subjected to gravity in Kinematic Simulation

## TL;DR

This study investigates how different energy spectrum laws influence the clustering behavior of inertial particles under gravity, revealing significant effects on attractor shapes and identifying a new attractor type for certain spectral conditions.

## Contribution

The paper introduces the impact of spectral power law variations on particle clustering and attractor formation, including the discovery of a new attractor type not seen in previous Kolmogorov spectrum studies.

## Key findings

- Spectral power laws significantly affect clustering attractor shapes.
- A new attractor type was identified for spectral power laws outside the Kolmogorov spectrum.
- Particle clustering varies with Stokes and Froude numbers across different spectra.

## Abstract

We study the clustering of inertial particles using a periodic kinematic simulation. Particles clustering is observed for different pairs of Stokes number and Froude number and different spectral power laws ($1.4 \leqslant p \leqslant 2.1$). The main focus is to identify and then quantify the effect of $p$ on the clustering attractor - by attractor we mean the set of points in the physical space where the particles settle when time tends to infinity. It is observed that spectral power laws can have a dramatic effect on the attractor shape. In particular, we observed a new attractor type which was not present in previous studies for Kolmogorov spectra ($p=5/3$).