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Letter to the Editor

Unstable interaction of gravity-inertial waves with Rossby waves with application to solar system atmospheres

J. F. McKenzie^1,2 and T. B. Doyle³

¹ King's College, University of Cambridge, UK
² School of Mathematical Sciences, University of KwaZulu-Natal, South Africa e-mail: mckenziej@ukzn.ac.za
³ Materials Research Division, iThemba LABS, Somerset West, South Africa e-mail: doyle@tlabs.ac.za

Received: 12 October 2009
Accepted: 12 January 2010

Abstract

This letter reports on the important features of an analysis of the combined theory of gravity – inertial – Rossby waves on a β-plane in the Boussinesq approximation. In particular, it is shown that the coupling between higher frequency gravity – inertial waves and lower frequency Rossby waves, arising from the accumulated influences of the β effect, stratification characterized by the Väisäla – Brunt frequency N, the Coriolis frequency f, and the component of vertical propagation wave number k_z, may lead to an unstable coupling between buoyancy – inertial modes with westward propagating Rossby waves. “Supersonic” fast rotators (such as Jupiter) are predicted to be unstable in a fairly narrow band of latitudes around their equators. The Earth is moderately supersonic and exhibits instability within about 34° of its equator. Slow “subsonic” rotators (e.g. Mercury, Venus, and the Sun's corona) are unstable at all latitudes except those very close to the poles where the β effect vanishes.