Vertical distribution of swimming particles within shallow flows

Abstract

We report on the vertical distribution of swimming particles in three-dimensional shallow flows obtained by numerical simulations. This study examines shallow flows generated by horizontally forcing a thin fluid layer. These flows are characterized by a Reynolds number related to the forcing ( Re F ) and the aspect ratio ( δ ) of the vertical to horizontal length scales. With increasing Re F δ 2 , the flow transitions from a steady, organized array of vortices to an unsteady disordered flow. For steady and unsteady flows, regions with upwellings and downwellings emerge. The particles swim only vertically with the aim of reaching a target depth, with their speed only depending on the distance from the target depth. Two target depths are considered: one close to the surface and the other near the bottom. Whether in steady or unsteady flow, particles swimming toward the upper target depth accumulate in downdrafts, while those moving toward the lower target depth accumulate in updrafts. In steady flows, this organization does not significantly affect how swimmers are vertically distributed. Many of them remain trapped in stable flow patterns and do not reach the target depth. In unsteady flow, the distributions of swimmers differ significantly. Particles are quickly displaced from the target depth after arrival, either being lifted by updrafts in vorticity-dominated regions or pushed down by downdrafts in strain-dominated regions. These observations are further confirmed using a kinematic flow model which indeed attributes the distribution of swimmers in the fluid layer to both flow unsteadiness and updrafts and downdrafts.