LAGRANGIAN DYNAMICS AND THE PARCEL METHOD IN ATMOSPHERIC MODELS

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Abstract
The Lagrangian “parcel method” of stability analysis is systematically presented and rendered rigorous in its application to nondivergent flow on a plane with constant Coriolis parameter. The method is applied in detail to two familiar models. (1) Zonal geostrophic current with linear horizontal shear. Here the parcel method is valid only for uniform initial disturbance (“infinite wave-length”), in which case the usual stability criterion applies, −ζg Anticyclonic vortex with concentric circular contours. Here, the parcel-method stability criterion is −ζg < f/2 (as suggested by the balance equation) and is valid for any initial disturbance with balanced velocity field. So far, no non-symmetric solution to the balance equation for this pressure field has been discovered.

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