Apparent absolute instability and the continuous spectrum

Abstract

The role of the continuous spectrum and its associated potential vorticity (PV) in absolute instability are investigated in the context of a semi-infinite version of Eady's basic state. This flow crudely resembles the zonally averaged midlatitude atmosphere. The disturbances are composed of a zero PV part and a nonzero PV part. A closed form analytic solution is described that features a localized wave packet whose streamfunction field expands and amplifies in an absolutely unstable way. However, since an examination of the PV field associated with this disturbance reveals that the linear amplification of the localized streamfunction wave packet is induced by a nonlocalized PV field, it is c..