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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 behavior is examined and compared to that of other known models. The linearised equations as well as long-wave approximations are presented.
Compelli, A. & Ivanov, R.I. (2016). The dynamics of flat surface internal geophysical waves with currents. Journal of Mathematic Fluid Mechanics 2016, pp.1-6. (doi:10.1007/s00021-016-0283-4