A model with constant vorticity in the liquid phase has been applied to the study of interfacial waves between two inviscid fluids in relative motion, in order to take into account the shear induced into the liquid by the concurrent gas flow. For a range of values of gas velocity and vorticity in the liquid phase a new wave pattern is calculated, consisting of a recirculating eddy below the wave crest. It is suggested that, under certain conditions, the onset of this new type of waves (rather than the classical Kelvin-Helmholtz instability mechanism) provides the inviscid analog to the experimentally observed transition to roll waves.