Schooling Fish in Challenging Geometries

Fish often congregate into cohesive groups to navigate environments efficiently and safely, exhibiting various forms of collective motion such as milling, polarized schooling, and turning. Many computational models have been proposed to uncover the mechanisms behind these fascinating phenomena, though most focus on fish schools in unbounded domains. However, to understand how fish navigate and discover complex undersea structures like caves and tunnels, it is essential to formulate models of fish schools in confined domains. Here, we use high-order boundary integral equations to achieve non-penetration boundary conditions for 2D potential flow. We investigate how fish schools behave under confinement, with a narrow channel connecting two semicircular chambers. We examine the effects of this complex geometry on collective behavior, including the splitting and transition between the two chambers. We find surprising interplay between school size and school escape dynamics. Our models and results pave the way towards understanding survival strategies and collective behavior in challenging environments.