title: 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.
authors.affiliation: Dipartimento di Fisica and Istituto Nazionale di Fisica Nucleare, Università "Tor Vergata," Via della Ricerca Scientifica 1, I-00133 Roma, Italy.
authors.forename: Massimo
authors.initials: M
authors.lastname: De Pietro
authors.affiliation: Department of Applied Physics, J. M. Burgerscentrum, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands.
authors.forename: Michel A T
authors.initials: MA
authors.lastname: van Hinsberg
authors.affiliation: Dipartimento di Fisica and Istituto Nazionale di Fisica Nucleare, Università "Tor Vergata," Via della Ricerca Scientifica 1, I-00133 Roma, Italy.
authors.forename: Luca
authors.initials: L
authors.lastname: Biferale
authors.affiliation: Department of Applied Physics, J. M. Burgerscentrum, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands.
authors.forename: Herman J H
authors.initials: HJ
authors.lastname: Clercx
authors.affiliation: TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, Narsingi, Hyderabad 500075, India.
authors.forename: Prasad
authors.initials: P
authors.lastname: Perlekar
authors.affiliation: Department of Applied Physics and Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands and IAC, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, I-00185 Roma, Italy.
authors.forename: Federico
authors.initials: F
authors.lastname: Toschi
mesh_terms: D057446:Hydrodynamics; D055595:Mechanical Phenomena; D008962:Models, Theoretical