Past Event: Oden Institute Seminar

Coarse-grained models for interacting flapping swimmers

Anand Oza, Professor, New Jersey Institute of Technology

Abstract

I will present the results of a theoretical investigation into the dynamics of interacting flapping swimmers. Our study is motivated by ongoing experiments in the Applied Math Lab at the Courant Institute, in which freely-translating, heaving hydrofoils interact hydrodynamically to choose their relative positions and velocities. We develop a discrete dynamical system in which flapping swimmers shed point vortices during each flapping cycle, which in turn exert forces on the swimmers. We present a framework for finding exact solutions to the evolution equations and for assessing their stability, giving physical insight into the preference for certain observed "schooling states". The model may be extended to arrays of flapping swimmers, and to configurations in which the swimmers' flapping frequencies are incommensurate. Generally, our results indicate how hydrodynamics may mediate schooling and flocking behavior in biological contexts.