Clustering of vertically constrained passive particles in homogeneous, isotropic turbulence

TL;DR

This study investigates how vertical confinement affects the clustering behavior of passive particles in 3D turbulence, revealing an optimal confinement level that maximizes particle clustering.

Contribution

Introduces a simple model for particle dynamics under vertical confinement in turbulence, analyzing the effects on clustering and compressibility across different confinement levels.

Findings

Maximum clustering occurs at a specific confinement strength.

Vertical confinement induces effective compressibility in particle trajectories.

Clustering is optimized when the slab depth is a few times the Kolmogorov length.

Abstract

We analyze the dynamics of small particles vertically confined, by means of a linear restoring force, to move within a horizontal fluid slab in a three-dimensional (3D) homogeneous isotropic turbulent velocity field. The model that we introduce and study is possibly the simplest description for the dynamics of small aquatic organisms that, due to swimming, active regulation of their buoyancy, or any other mechanism, maintain themselves in a shallow horizontal layer below the free surface of oceans or lakes. By varying the strength of the restoring force, we are able to control the thickness of the fluid slab in which the particles can move. This allows us to analyze the statistical features of the system over a wide range of conditions going from a fully 3D incompressible flow (corresponding to the case of no confinement) to the extremely confined case corresponding to a two-dimensional slice. The background 3D turbulent velocity field is evolved by means of fully resolved direct numerical simulations. Whenever some level of vertical confinement is present, the particle trajectories deviate from that of fluid tracers and the particles experience an effectively compressible velocity field. Here, we have quantified the compressibility, the preferential concentration of the particles, and the correlation dimension by changing the strength of the restoring force. The main result is that there exists a particular value of the force constant, corresponding to a mean slab depth approximately equal to a few times the Kolmogorov length scale, that maximizes the clustering of the particles.