Spatial distribution of depth-directed swimmers within shallow flows

We investigate the behavior of swimming particles in a 3D shallow flow by numerical simulations and Lagrangian tracking. The particles swim vertically to reach a specific depth, either close to the bottom or the surface. This behavior is like that of bottom-dwelling zooplankton in shallow environments. In the horizontal, they strictly follow the flow which is confined to a thin fluid layer bounded vertically by rigid boundaries. The flow has a horizontal extent much larger than the layer depth and consists of several shallow vortices with updrafts in their cores and downdrafts at their peripheries. Statistics of particle positions and velocities reveal distinctive distribution patterns. The swimmers aiming to reach the lower depth accumulate in the updrafts, while the swimmers aiming to reach the upper depth accumulate in the downdrafts. The swimmers in the updrafts form tree-like structures that extend in the vertical direction, whereas swimmers in the downdrafts form thin structures that are elongated in the horizontal direction. The distribution patterns are a result of the interaction of the underlying flow features and the swimming capability of the particles, and they are reproduced using an idealized kinematic flow allowing us to explain the governing dynamics.