  We investigate strongly nonlinear stationary gravity waves which experience
refraction due to a thin vertical shear layer of horizontal background wind.
The velocity amplitude of the waves is of the same order of magnitude as the
background flow and hence the self-induced mean flow alters the modulation
properties to leading order. In this theoretical study, we show that the
stability of such a refracted wave depends on the classical modulation
stability criterion for each individual layer, above and below the shearing.
Additionally, the stability is conditioned by novel instability criteria
providing bounds on the mean-flow horizontal wind and the amplitude of the
wave. A necessary condition for instability is that the mean-flow horizontal
wind in the upper layer is stronger than the wind in the lower layer.
