  In this paper we develop an existence theory for small amplitude, steady,
two-dimensional water waves in the presence of wind in the air above. The
presence of the wind is modeled by a Kelvin--Helmholtz type discontinuity
across the air--water interface, and a corresponding jump in the circulation of
the fluids there. We consider both fluids to be inviscid, with the water region
being irrotational and of finite depth. The air region is considered with
constant vorticity in the case of infinite depth and with a general vorticity
profile in the case of a finite, lidded atmosphere.
