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The viscous nonlinear symmetric baroclinic instability of a zonal shear flow

Published online by Cambridge University Press:  29 March 2006

I. C. Walton
I. C. Walton
Affiliation:
Department of Mathematics, University College London Present address: Department of Mathematics, Imperial College, London.
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Abstract

The stability of a baroclinic zonal current to symmetric perturbations on a meridionally unbounded f-plane is considered. The lower boundary is at rest but the upper one moves with a constant velocity in keeping with the velocity of the zonal current. Following Stone (1966) a horizontal length scale O(Ro) is taken, where Ro is the Rossby number, with the Richardson number Ri = O(1). Instability sets in when the wavelength is O(E1/3), where E is the Ekman number based on the distance between the rigid horizontal boundaries, which corresponds to Stone's inviscid value zero, and to McIntyre's (1970) value infinity on a length scale O(E½).

A nonlinear analysis about the point of onset of instability yields the result that for the monotonic mode zonal momentum is convected polewards. The possible implications of this result for the dynamics of Jupiter's atmosphere are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 68 , Issue 4 , 29 April 1975 , pp. 757 - 768
Copyright
© 1975 Cambridge University Press

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