Abstract
A geostrophic wind field is assumed, constant in time, with a jet-profile in the form of a parabola. From an arbitrary latitude a parcel is given an arbitrary finite perturbation from its equilibrium velocity, and the resulting motion of the parcel is studied. Two methods are used: that of classical dynamics, and the modern phase-plane analysis for non-linear systems; and the generality of the latter method in hydrodynamics is emphasized. For a middle-latitude perturbation a precise non-linear condition of instability is formulated, and the meteorologically significant oscillations are examined in detail. Low-latitude perturbations, in which the Coriolis parameter varies linearly with latitude, are also discussed. Sample trajectories are exhibited for the different types of oscillations.
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