  In 1957 Crapper found an exact solution for capillary waves propagating at
the surface of an irrotational flow of infinite depth. Here we provide
conclusive analytical and numerical evidence that a Crapper wave makes the
profile of a periodic traveling wave propagating, in the absence of the effects
of gravity and surface tension, in a constant vorticity flow. This is achieved
by constructing a Stokes expansion up to the third order in a small amplitude
parameter and by numerically computing large amplitude waves.
