  We examine a two-media 2-dimensional fluid system consisting of a lower
medium bounded underneath by a flatbed and an upper medium with a free surface
with wind generated surface waves but considered bounded above by a lid by an
assumption that surface waves have negligible amplitude. An internal wave
driven by gravity which propagates in the positive $x$-direction acts as a free
common interface between the media. The current is such that it is zero at the
flatbed but a negative constant, due to an assumption that surface winds blow
in the negative $x$-direction, at the lid. We are concerned with the layers
adjacent to the internal wave in which there exists a depth dependent current
for which there is a greater underlying than overlying current. Both media are
considered incompressible and having non-zero constant vorticities. The
governing equations are written in canonical Hamiltonian form in terms of the
variables, associated to the wave (in a presence of a constant current). The
resultant equations of motion show that wave-current interaction is influenced
only by the current profile in the 'strip' adjacent to the internal wave.
