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We examine a two-media 2-dimensional fluid system consisting of a lowermedium bounded underneath by a flatbed and an upper medium with a free surfacewith wind generated surface waves but considered bounded above by a lid by anassumption that surface waves have negligible amplitude. An internal wavedriven by gravity which propagates in the positive $x$-direction acts as a freecommon interface between the media. The current is such that it is zero at theflatbed but a negative constant, due to an assumption that surface winds blowin the negative $x$-direction, at the lid. We are concerned with the layersadjacent to the internal wave in which there exists a depth dependent currentfor which there is a greater underlying than overlying current. Both media areconsidered incompressible and having non-zero constant vorticities. Thegoverning equations are written in canonical Hamiltonian form in terms of thevariables, associated to the wave (in a presence of a constant current). Theresultant equations of motion show that wave-current interaction is influencedonly by the current profile in the 'strip' adjacent to the internal wave.

Hamiltonian Approach to Internal Wave-Current Interactions in a Two-Media Fluid with a Rigid Lid