Controlled Hydrodynamic Interactions in Schooling Aquatic Locomotion

We present experimental data elucidating the effects of hydrodynamic coupling on the propulsive efficiency of an array of three oscillating hydrofoils. We simulate this system using an inviscid flow model; this model duplicates certain key features of our experimental data but fails to consider the effects of wake vortex generation and interaction. We present a qualitative model for the role played by wake vortex dynamics in the cooperative locomotion of fish schools, and derive a mathematical model in the form of a nonlinear control system describing the interaction of a single deformable body with a single nearby vortex. We present simulations based on the latter to illustrate the capture of vortices shed from one fish in a school by a second, trailing fish; vortex capture in this sense is the control problem central to cooperative swimming.