Hamiltonian Approach to the Modeling of Internal Geophysical Waves with Vorticity

We examine a simplified model of internal geophysical waves in a rotational 2-dimensional water-wave system, under the influence of Coriolis forces and with gravitationally induced waves. The system consists of a lower medium, bound underneath by an impermeable flat bed, and an upper lid. 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 its conjugate variables and perform a variable transformation to show that it has canonical Hamiltonian structure. We then linearize the system, determine the equations of motion of the linearized system and calculate the dispersion relation. Finally, limiting cases are examined to recover irrotational and single medium systems as well as an infinite 2 media system.