Effect of Stratification and Background Flow on the Frequency of Rossby Basin Modes in Presence of Bottom Topography

This work attempts to express the change, induced by the introduction of stratification, of the Rossby eigen-modes of a closed basin with bottom topography, filled with a uniform fluid in the unperturbed configuration. Such a modification has been found in the output of a set of numerical experiments on the Argentine Basin and then computed analytically: stratification has been introduced in the mathematical form of a perturbation of a homogeneous fluid over a non flat bottom. It has been found that the eigen-modes lose their barotropic character and differences appear in the dynamical fields (velocity and pressure) from upper to lower layer. Moreover, the frequency of the modes changes; an analytical expression of this frequency correction as a function of stratification has been found. The impact on modal frequency of a geostrophic background flow has also been computed analytically. Some simple analytical results for an elementary geometrical setting have been determined.