  The two-dimensional free-boundary problem describing steady gravity waves
with vorticity on water of finite depth is considered. It is proved that no
small-amplitude waves are supported by a horizontal shear flow whose free
surface is still in a coordinate frame such that the flow is time-independent
in it. The class of vorticity distributions for which such flows exist includes
all positive constant distributions, as well as linear and quadric ones with
arbitrary positive coefficients.
