Collective Transitions of Schooling Fish in a Two-Chamber Domain

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 model fish as dipolar fields and use high-order boundary integral equations to achieve slip boundary conditions for 2D potential flow. We explore the behavior of fish schools in a two-chamber confined environment, modeled as a dumbbell-like domain featuring two circular chambers connected by a narrow channel. We examine the effects of this complex geometry on collective behavior, including transitions 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.