Bound states of asynchronously flapping tandem wings

We present the results of a theoretical investigation into the dynamics of tandem flapping wings, a model system for studying schooling swimmers in relatively fast flows. We develop a discrete dynamical system in which the swimmers are modeled as wings that shed point vortices in an irrotational and inviscid flow. Our model may readily be generalized to account for configurations in which the wings' flapping amplitudes and frequencies are incommensurate. We find that the wings may either separate, collide, or form unsteady bound states, and we compare our theoretical predictions with recent experiments. Generally, our results indicate how hydrodynamics may influence the dynamics of schooling swimmers in biological contexts.