Clustering of vertically constrained passive particles in homogeneous isotropic turbulence

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 η, that maximizes the clustering of the particles.

Large-scale confinement and small-scale clustering of floating particles in stratified turbulence

“…In the absence of fluctuations (θ = 0) this equation would simply represent the linear relaxation of particles towards the isopycnal layer z = 0 [22]. This is not achieved since the term ∂θ/∂z is fluctuating without a definite sign.…”

“…Little is known about the distribution of floating particles in stratified turbulence, in spite of its relevance for applications. Recent works have studied the effect of stratification on the clustering of heavy [18] and light [19] particles, the formation of tangling clustering in stratified turbulence [20,21], and the effect of a vertical confinement in homogeneous turbulence [22].One of the most remarkable examples of confinement of particles in the ocean is the formation of the so-called thin phytoplankton layers (TPLs): aggregations of phytoplankton and zooplankton at high concentration with thickness from centimeters to few meters, extending up to several kilometers horizontally and with a time scale from hours to days [23]. Among the possible mechanisms of formation of TPLs, convergence to a depth of neutral buoyancy has been proposed for nonswimming species and aggregates, such as diatoms and marine snow, which are often observed to accumulate in the presence of strong stratification [24].…”

“…Little is known about the distribution of floating particles in stratified turbulence, in spite of its relevance for applications. Recent works have studied the effect of stratification on the clustering of heavy [18] and light [19] particles, the formation of tangling clustering in stratified turbulence [20,21], and the effect of a vertical confinement in homogeneous turbulence [22].…”

Spatial population genetics with fluid flow

“…[32], when the generation time (τ g ) of reproducing organisms such as plankton is longer than the time it takes for the flow to transport them over a distance of the order of the thickness of the thin layer, then microorganisms will experience an effectively compressible, almost two-dimensional velocity field. Importantly, the fact that the size of the organism itself is much smaller than the thickness of the layer is not relevant in this regard [38]. A simplified model demonstrating that vertical confinement induces an effective compressibility is based on the idea of an organism with a given population density that is transported in a stratified fluid.…”

Directed-bond percolation subjected to synthetic compressible velocity fluctuations: Renormalization group approach

“…Recently, there has been increased interest in different advection problems in compressible turbulent flows [18,19,20,21]. These studies show that compressibility plays an important role for population dynamics or chaotic mixing of colloids.…”