  Propagation of surface waves on a background shear flow with constant
vorticity is studied and compared against the case when the background flow is
uniform in depth. For a shear flow with the linear vertical profile, the
dispersion relation of surface gravity waves is minutely analyzed for a fluid
of finite depth. Under the assumption that the background flow gradually varies
in the horizontal direction, the primary attention is paid to the wave blocking
phenomenon; the effect of vorticity on this phenomenon is studied in details.
The conditions of wave blocking are obtained and categorized for different
values of the governing dimensionless parameters.
