Waves and resonance in free-boundary baroclinic instability

Abstract

Eady's model of baroclinic instability has been generalized by including β (the meridional gradient of planetary potential vorticity) while assuming that total potential vorticity is uniform. Moreover, the problems of Eady and of Phillips have been enriched by including a fixed topography or a free boundary (which implies a flow-dependent geostrophic topography). The most general cases (with β, fixed topography and a free boundary) of both problems are shown to have nearly identical stability properties, mainly determined by two Charney numbers: the planetary one and a topographic one. The question of whether this generalized baroclinic instability problem can be described by wave resonance or component ‘resonance’ is addressed. By waves are meant physical modes, which could freely propagate by themselves but are effectively coupled by an independent basic shear, producing the instability. Components, on the other hand, are mathematical modes for which the shear is also crucial for their existence, not just for their coupling, hence the quotation marks around ‘resonance’. In this paper it is shown that both scenarios, components ‘resonance’ and waves resonance, cast light on the free-boundary baroclinic instability problem by providing explanations of the instability onset (at minimum shear) and maximum growth rate cases, respectively. The importance of the mode pseudomomentum for the fulfillment of both mechanisms is also stressed.