  We examine a two dimensional fluid system consisting of a lower medium
bounded underneath by a flatbed and an upper medium with a free surface. The
two media are separated by a free common interface. The gravity driven surface
and internal water waves (at the common interface between the media) in the
presence of a depth-dependent current are studied under certain physical
assumptions. Both media are considered incompressible and with prescribed
vorticities. Using the Hamiltonian approach the Hamiltonian of the system is
constructed in terms of 'wave' variables and the equations of motion are
calculated. The resultant equations of motion are then analysed to show that
wave-current interaction is influenced only by the current profile in the
'strips' adjacent to the surface and the interface. Small amplitude and
long-wave approximations are also presented.
