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A fluid system consisting of two domains is examined. The system is considered as being bounded at the bottom and top by a flatbed and wave-free surface respectively. An internal wave propagating in one direction, driven by gravity, acts as a free common interface between the fluids. Various current profiles are 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 formulated. The presented models provide potential applications to modelling of internal geophysical waves.
Compelli, A., Ivanov, R. (2017) Models of internal waves in the presence of currents, Pliska Stud. Math. Bulgar. 26 (2016) 99–112. Paper published by Dublin Institute of Technology in association with ESHI (Dublin).