Eur. Phys. J. Plus (2011) 126: 36
https://doi.org/10.1140/epjp/i2011-11036-6

Regular Article

A note on long Rossby waves on a quiescent abyss

¹ ISMAR-CNR, viale Romolo Gessi 2, 34123, Trieste, Italy
² ISAC-CNR, via Fosso del Cavaliere, 100, 00133, Roma, Italy

^* e-mail: f.crisciani@ismar.cnr.it

Received: 23 November 2010
Accepted: 3 March 2011
Published online: 12 April 2011

Abstract

The framework of the investigation is the propagation of quasi-geostrophic Rossby waves in a two-layer ocean, within the -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 -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.