  Special features of surface gravity waves in deep fluid flow with constant
vertical shear of velocity is studied. It is found that the mean flow velocity
shear leads to non-trivial modification of surface gravity wave modes
dispersive characteristics. Moreover, the shear induces generation of surface
gravity waves by internal vortex mode perturbations. The performed analytical
and numerical study provides, that surface gravity waves are effectively
generated by the internal perturbations at high shear rates. The generation is
different for the waves propagating in the different directions. Generation of
surface gravity waves propagating along the main flow considerably exceeds the
generation of surface gravity waves in the opposite direction for relatively
small shear rates, whereas the later wave is generated more effectively for the
high shear rates. From the mathematical point of view the wave generation is
caused by non self-adjointness of the linear operators that describe the shear
flow.
