  The swimming of an elliptical disk at small Reynolds number is studied on the
basis of a perturbative solution of the Navier-Stokes equations for fluid flow
near a deformable infinite sheet. A stroke involving an elliptically polarized
plane surface wave is studied, in extension of work by Taylor and Tuck. In
general the elliptic polarization of the stroke leads to an asymmetry of the
flow in the upper and lower half-space. On the basis of results for an infinite
sheet expressions for the mean translational and rotational swimming velocity
of an elliptical disk of size much larger than the wavelength of the stroke are
deduced. In addition expressions are derived for the mean power and the
efficiency of swimming.
