On the motion of a non-rigid sphere in a perfect fluid (Q1897723)

The paper deals with the problem of the motion of a slightly deformable sphere embedded in a non-uniform potential flow field. The Hamiltonian system of the governing nonlinear differential equations is derived up to the first-order with respect to the small amplitude of the volume- preserving surface deformation . One demonstrates that the equations for the linear and angular velocities are decoupled. The authors point out the qualitative difference between the self- propulsion of a deformable sphere in a quiescent or uniform surrounding, and that in a non-uniform ambient flow field. The effect is more significant in the latter case. Also discussed is the corresponding parametric resonant interaction as a possible mechanism for self- propulsion. The motion of the deformable sphere in the proximity of a pulsating bubble, as well as the motion in the gravitational field of water waves, illustrate the resonant self-propulsive interactions.