Swimming of a bendable foil in potential flow

The dynamic behavior of a Joukowski-type foil undergoing rhythmic bilateral bending in an inviscid fluid is investigated to explore the unidirectional swimming of streamlined bodies performing asymmetric oscillatory deformations in a potential flow without vortex shedding. To this end, the velocity potential induced by the C-shaped bending of the foil is derived through a novel approach to boundary function treatment, and the hydrodynamic loads are subsequently obtained using modified Sedov formulas. The equations of motion for the rhythmic-bending foil reveal that through autonomous control of its own rotation coupled with center-of-mass shift, the foil can achieve unidirectional undulatory translation without transient retrograde motions.