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.
The Applicability of the Piecewise Linear Current Profile in the Baroclinic Instability Problem