We therefore employ a two layer model to mimic the "real ocean" stratified dynamics. Using an eigenvalue solver we have determined the normal modes of the basin, and studied their sensitivity with respect to some key physical quantities.
The modes found with the two layer model belong to two classes that resemble, respectively, the properly defined barotropic and baroclinic modes of a two layer fluid in the flat bottom case. We have examined the sensitivity of the barotropic-like modes with respect to layers density difference and interface depth; their period is monotonically increasing, both with respect to a shoaling interface and a decreasing layers density difference. The spatial patterns of the modes seem, on the contrary, virtually insensitive respect to the above parameters and also very close to the ones obtained with the barotropic model. Nonetheless, the changes are too small to account for the discrepancy between a 25-day mode from observations and a 31-day normal mode from our shallow-water model.