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A Hamiltonian model for the propagation of internal water waves interactingwith surface waves, a current and an uneven bottom is examined. Using theso-called Dirichlet-Neumann operators, the water wave system is expressed inthe Hamiltonian form, and thus the motions of the internal waves and surfacewaves are determined by the Hamiltonian formulation. Choosing an appropriatescaling of the variables and employing the Hamiltonian perturbation theory fromHamiltonian formulation of the dynamics, we derive a KdV-type equation withvariable coefficients depending on the bottom topography to describe theinternal waves.

Hamiltonian model for coupled surface and internal waves over currents and uneven bottom