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Applied mathematics, Fluids and plasma physics
We provide a Hamiltonian formulation for the governing equations describing the two-dimensional nonlinear interaction between coupled surfacewaves, internalwaves, and an underlying current with piecewise constant vorticity, in a two-layered fluid overlying a flat bed. This Hamiltonian structure is a starting point for the derivation of simpler models, which can be obtained systematically by expanding the Hamiltonian in dimensionless parameters. These enable an in-depth study of the coupling between the surface and internal waves, and how both these wave systems interact with the background current.
A. Constantin and R. I. Ivanov, A Hamiltonian approach to wave-current interactions in two-layer fluids, Physics of Fluids 27, 086603 (2015); doi:10.1063/1.4929457