A note on long Rossby waves on a quiescent abyss

Abstract.

The framework of the investigation is the propagation of quasi-geostrophic Rossby waves in a two-layer ocean, within the $\beta$ -plane approximation. The propagation of long Rossby waves in the upper layer is considered, while the lower layer represents a hypothetical resting abyss. It is shown, by means of a systematic scale analysis, that this model implies that the depth of the permanent pycnocline relative to the total ocean depth is of the same order of magnitude as a typical parameter inherent to the $\beta$ -plane approximation. From the quantitative point of view, there is a full accordance between the depth of the permanent pycnocline so estimated and the real one. The phase velocity of the so-obtained long Rossby waves, which are non-dispersive, results to be closer to observations than the phase velocity of the first baroclinic mode of long Rossby waves in a continuously stratified ocean. We point out also that the same kind of propagation of a standard Rossby wave would require an unrealistically small thickness of the upper layer. Thus, in the latter case, Rossby waves necessarily propagate also in the lower layer.