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We examine a 2-dimensional water-wave system, with gravitationally induced waves, consisting of a lower medium bound underneath by an impermeable flat bed and an upper medium bound above by an impermeable lid such that the 2 media have a free common interface. Both media have constant density and constant (non-zero) vorticity. By examining the governing equations of the system we calculate the Hamiltonian of the system in terms of it's conjugate variables and per- form a variable transformation to show that it has canonical Hamiltonian structure.
Compelli, A. (2014) Hamiltonian Formulation of 2 Bounded Immiscible Media with Constant Non-Zero Vorticities and a Common Interface, Wave Motion, to appear. doi: 10.21427/8q5f-2e54