  A two-dimensional water wave system is examined consisting of two discrete
incompressible fluid domains separated by a free common interface. In a
geophysical context this is a model of an internal wave, formed at a pycnocline
or thermocline in the ocean. The system is considered as being bounded at the
bottom and top by a flatbed and wave-free surface respectively. A current
profile with depth-dependent currents in each domain is considered. The
Hamiltonian of the system is determined and expressed in terms of canonical
wave-related variables. Limiting behaviour is examined and compared to that of
other known models. The linearised equations as well as long-wave
approximations are presented.
