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Original Research Papers

Instability of very long waves in a zonal flow


John W. Miles

Institute of Advanced Studies, Australian National University, AU
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The eigenvalue problem governing baroclinic disturbances, relative to a zonal flow, of wavelengths comparable with the circumference of the Earth is formulated on the basis of: (a) adiabatic, frictionless motion of a perfect gas in a uniform gravitational field over a spherical Earth and (b) the restriction Ro < Ri−1/2 <1, where Ro and Ri are appropriate Rossby and Richardson numbers. Attention is focused on unstable disturbances, and several theorems governing the existence of such disturbances are deduced from an earlier and more general study of baroclinic stability. Explicit results for the complex wave speed of an unstable disturbance are given in the limits β → 0 and β → ∞, where β = Ro Ricotφ (φ = latitude). It is established that one and only one unstable mode exists for a wide class of monotonically increasing wind profiles.

How to Cite: Miles, J.W., 2012. Instability of very long waves in a zonal flow. Tellus A: Dynamic Meteorology and Oceanography, 17(3), pp.302–305. DOI:
Published on 01 Jan 2012.
Peer Reviewed


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