Self-Propulsion of a Spherical Body Shedding Coaxial Vortex Rings in an Ideal Fluid: Hamiltonian Modeling and Simulation

We present a model for the self-propulsion of a spherical body shedding circular vortex rings in an ideal fluid. Rings are shed from a moving ridge on the body's surface; timed oscillations of this ridge mimic the pulsing of a swimming medusan jellyfish. We regard the velocity of the ridge relative to the center of the body as a control parameter, and we demonstrate the relative efficacy of four distinct propulsive gaits. The model exploits the recently documented Hamiltonian structure underpinning the dynamic interaction of an arbitrary smooth body with a collection of closed vortex filaments of arbitrary shape.