Hydrodynamic interactions between fish swimming against a flow

Several fish species can successfully orient and swim against an incoming flow (rheotaxis), alone or in groups. At the intersection of the phenomena of schooling and rheotaxis, we examine the role of hydrodynamics in enabling fish to maintain stable schooling formations against an incoming flow. First, we develop a mathematical model of a fish pair, swimming in an infinite channel against an imposed background flow. The local flow alters the fish movement through advection, while the self-propulsion of the fish, modeled as vortex dipoles, influence each other as well as the local flow field. The established dynamical system for the spatial configuration and orientation of the fish is analyzed to determine stable and unstable swimming formations under different flow conditions. The study reveals a stable configuration of in-tandem swimming when fish are at a larger streamwise distance from each other and a specific staggered formation when the fish are at a closer streamwise distance. The precisely parallel side-by-side swimming configuration is shown to be unstable under all conditions, in the absence of visual cues. Finally, preliminary experiments are discussed to help calibrate the model and validate the findings of the study.