Self-propulsion of a deformable ellipse with the controllable rotation through inviscid fluids

Abstract

Self-propulsion of a deformable ellipse immersed in an unbounded inviscid fluid is discussed in order to explore the effect of the deformation and controlled rotation of the body coupled with the shift of its internal mass on the self-motion. The ellipse is capable of symmetric deformation along the two orthogonal axes and endowed with some self-regulation ability via the shift and rotation of its internal mass. From the model, the appropriate velocity potential induced by the motion of the ellipse with the deformation in an otherwise undisturbed fluid is derived, and then the equations of motion are obtained by means of integrals of the unsteady fluid pressure. The equations are utilized to explore self-translational behaviors of the ellipse through the cyclic shift of its internal mass and deformation coupled with its own controllable rotation. Analysis and numerical results show that the ellipse can break the kinematic time-reversal symmetry by properly adjusting its own rotation to coordinate with the deformation and the cyclic shift of the inner mass to meet a forward criterion, and push itself to move persistently forward without a regression at zero system momentum, exhibiting some basic serpentine movements according as the ellipse performs complete revolutions or oscillates between two extreme yaw angles during its self-motion.