Wave-Packet Resonance: Instability of a Localized Barotropic Jet

Abstract

A better physical understanding of the instability of a zonally varying basic flow may be gained by invoking the concept of wave-packet resonance, which complements the notions of absolute and convective instability. To highlight the nature of such instability, a generic barotropic jet that has essentially only two closed contours in its basic vorticity gradient field is analyzed. Apart from the structure of the jet itself, the domain-averaged zonal flow component and the beta effect are two determining factors that control the form of wave-packet resonance. These factors influence the propagation characteristics of an unstable disturbance. When their influences counterbalance one another, the instability is attributable to stationary wave-packet resonance; otherwise it is due to propagating wave-packet resonance. This model setting illustrates that a local mode may have a finite group velocity and the self-reseeding of a disturbance does not necessarily require recycling through the streamwise boundaries. The detailed properties of the unstable modes are examined in terms of their structure, propagating characteristics, and local energetics.