Lagrangian flow networks for passive dispersal: tracers versus finite-size particles

Passive dispersal of different materials in ocean flows has gotten considerable attention over the last decade to increase our knowledge about the distribution of seeds plants among islands and coastal areas, the transport of larvae of different organisms between habitats and the transport of litter. Most studies have treated these objects as tracers to investigate distribution patterns and connectivity between different areas. We compare this approach with a study that considers the objects' size and density and discusses the deviation from the tracer approach. To this end, we introduce a two-dimensional kinematic velocity field which allows us to study the connectivity between an arbitrary number of islands located at arbitrary but prescribed positions in an open flow of a given direction. First, the mixing induced by the islands, which act as obstacles in the flow, was accounted for with the inclusion of a von K\'arm\'an vortex street in the wake of each island. Furthermore, we accounted for the size and density of particles approximated as spheres. Finally, we treated the particles as inertial particles experiencing various forces in the flow and computed their trajectories in a given flow field by solving the Maxey-Riley equations. In this way, we have constructed a Lagrangian flow network reflecting the connectivity between islands depending on the properties of the finite-size particles and comparing them with the motion of tracers. We show that the density differences, the flow properties, and the islands' position geometry substantially change the connectivity between islands. That change leads to segregating inertial particles according to their size and density. Nevertheless, the most striking observation is how the tracer transport (independently of geometry) overestimates the probabilities for specific pathways. In fact, the connectivity for inertial particles is much sparser than for tracers, such that certain pathways have extremely low probabilities; they practically do not exist. These results suggest that the transport probabilities can be highly under or overestimated by tracers' often-used approximation of inertial particles.