Self-propulsion of a free hydrofoil with localized discrete vortex shedding: analytical modeling and simulation

We present a model for the self-propulsion of a free deforming hydrofoil in a planar ideal fluid. We begin with the equations of motion for a deforming foil interacting with a pre-existing system of point vortices and demonstrate that these equations possess a Hamiltonian structure. We add a mechanism by which new vortices can be shed from the trailing edge of the foil according to a time-periodic Kutta condition, imparting thrust to the foil such that the total impulse in the system is conserved. Simulation of the resulting equations reveals at least qualitative agreement with the observed dynamics of fishlike locomotion. We conclude by comparing the energetic properties of two distinct turning gaits for a free Joukowski foil with varying camber.