Efficient foil propulsion through vortex control

We investigate the problem of a heaving and pitching hydrofoil in an inflow that consists of a uniform velocity field and a staggered array of vortices. The foil can exploit the energy in such a Karman vortex street for efficient propulsion of animals or submarines. Through a two-dimensional inviscid analysis, me find that the phase between foil motion and the arrival of inflow vortices is a critical parameter. Everything else being equal, the highest efficiency is seen when this phase is such that the foil moves in close proximity to the oncoming vortices. Different modes of vortex interaction in the wake results from a variation in this phase, and we show that the how downstream of the foil is related to the foil input power.