Hamiltonian structure for rotational capillary waves in stratified flows

We show that the governing equations of two-dimensional water waves driven by surface tension propagating over two-layered stratified flows admit a Hamiltonian formulation. Moreover, the underlying flows that we consider here, have piecewise constant distribution of vorticity, the jump in vorticity being located along the interface separating the fluid of bigger density at the bottom from the lighter fluid adjacent to the free surface.