Stability of passive locomotion in inviscid wakes

Abstract

We consider the passive locomotion of rigid bodies in inviscid point-vortex wakes. This work is motivated by a common belief that live and inanimate objects may extract energy from unsteady flows for locomotory advantages. Studies on energy extraction from unsteady flows focus primarily on energy efficiency. Besides efficiency, a fundamental aspect of energy extraction for locomotion purposes is stability of motion. Here, we propose idealized wake models using periodically generated point vortices to emulate shedding of vortices from an un-modeled moving or stationary object. We assess the stability of these point-vortex wakes and find that they are stable for a range of periods, unlike the von Kármán street model which is mainly unstable. We then investigate the dynamics of a rigid body submerged in such wakes. In particular, we calculate periodic trajectories where the rigid body "swims" passively against the flow by extracting energy from the ambient vortices. All the periodic trajectories we find are unstable. The largest instabilities reported are for elliptic bodies where rotational effects play a role in destabilizing their motion. Within the context of this model, we conclude that passive locomotion of rigid bodies in inviscid wakes is unstable. Questions as to whether passive stability can be achieved when accounting for fluid viscosity and body elasticity remain open. © 2013 American Institute of Physics.