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A Hamiltonian approach to wave-current interactions in two-layer fluids. (English) Zbl 1326.76021

Summary: We provide a Hamiltonian formulation for the governing equations describing the two-dimensional nonlinear interaction between coupled surface waves, internal waves, 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.{
©2015 American Institute of Physics}

MSC:

76B55 Internal waves for incompressible inviscid fluids
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
76B07 Free-surface potential flows for incompressible inviscid fluids
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