The structure and dynamics of simple models of swimming collectives

Fish schools are complex structures organized by the immersing fluid interacting with organismal sensing and behavior. How these aspects are integrated together by the school to yield its dynamics is a wide open question. I will discuss two types of models of swimming collectives, asking the simple question of what types of schools are stable under hydrodynamic interactions. Both types of models were inspired by experiments in the Courant Institute Applied Math Lab that studied the interactions of freely moving ensembles of wings. In one model we extend the seminal work of Weihs to study the dynamics and stability of one- and two-dimensional schools, with crystalline order, whose swimmers produce and interact with the collective vortical background flows. In the second model, we study a simplified version of the body/fluid dynamics, and move to a continuum setting. This model lays bare the role of time-delay in body-vortex interactions, which makes high Reynolds schooling much different from active suspensions at the micro-scale. We find and analyze traveling waves of swimmers, among other things.