Up a Creek Without a Paddle: Idealized Aquatic Locomotion via Forward Vortex Shedding

We present a model for the self-propulsion of a circular cylindrical vehicle through a planar ideal fluid. The input to the system is the relative angular velocity of a balanced rotor mounted above the vehicle’s center of mass. A Kutta condition is enforced regularly in time at a point along the edge of the vehicle, enabling the exchange of momentum between the vehicle and the surrounding fluid through discrete vortex shedding. Between vortex-shedding events, the dynamics of the vehicle and its wake are governed by a system of equations with non-canonical Hamiltonian structure. We present simulation results depicting the translational acceleration of the vehicle from rest as a result of sinusoidal oscillations in the position of the rotor, and we demonstrate that the propulsive efficiency of such oscillations exhibits a relative maximum at a certain driving frequency.