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Barotropic instability of the Bickley jet

Published online by Cambridge University Press:  26 April 2006

S. A. Maslowe
S. A. Maslowe
Affiliation:
Department of Mathematics, McGill University, Montreal, P.Q. H3A 2K6, Canada
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Abstract

The linear stability of the zonal shear flow $\overline{u} = - \sec h^2 y$ is investigated in the framework of the beta-plane approximation. This retrograde jet is known to be more unstable than its eastward-propagating counterpart and has some surprising characteristics. First, this is a rare example of a flow in which barotropically unstable modes occur that do not have a critical point. Secondly, singular neutral modes exist in which the critical point occurs at the centre of the jet, where $\overline{u}^{\prime}_{\rm c}=0 $. It is shown in this paper that such singular modes form part of the stability boundary both for the varicose mode and also for the radiating sinuous mode.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 229 , August 1991 , pp. 417 - 426
Copyright
© 1991 Cambridge University Press

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