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Wave-Packet Resonance: Instability of a Localized Barotropic Jet

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  • 1 Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, Illinois
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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.

Corresponding author address: Dr. Mankin Mak, Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, IL 61801. Email: mak@atmos.uiuc.edu

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.

Corresponding author address: Dr. Mankin Mak, Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, IL 61801. Email: mak@atmos.uiuc.edu

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