Inertial effects in small-amplitude swimming of a finite body

We study the mechanism of small-amplitude swimming of a deformable body of finite size in a viscous incompressible fluid described by the Navier-Stokes equations. The theory is based on a perturbation expansion in powers of the amplitude of surface displacements. A nonvanishing swimming velocity is found in second order perturbation theory. The average motion may include both a translational and a rotational contribution. For harmonic time variation of the first order flow we are led to a natural definition of the efficiency of swimming.