(112b) Swimming in Potential Flow

The well-known self-propulsion, or swimming, of a deformable body in Stokes flow (i.e. at low Reynolds number) can be understood and modeled from the variation in the configuration-dependent hydrodynamic resistance tensor throughout the period of deformation. Remarkably, at the other extreme of high-Reynolds number inviscid or potential flow, a deformable body may also self-propel without doing any work on the fluid. As a body deforms the mass of fluid displaced – the so-called added mass – depends on the instantaneous body configuration and a net displacement is possible over a period of deformation. We show that this potential-flow swimming takes a form identical to that for Stokes swimmers with the configuration-dependent added mass replacing the resistance tensor.