  We consider the wind-forced nonlinear Schroedinger (NLS) equation obtained in
the potential flow framework when the Miles growth rate is of the order of the
wave steepness. In this case, the form of the wind-forcing terms gives rise to
the enhancement of the modulational instability and to a band of positive gain
with infinite width. This regime is characterised by the fact that the ratio
between wave momentum and norm is not a constant of motion, in contrast to what
happens in the standard case where the Miles growth rate is of the order of the
steepness squared.
