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On the instability of sheared disturbances

Published online by Cambridge University Press:  21 April 2006

Peter H. Haynes
Peter H. Haynes
Affiliation:
Joint Institute for the Study of the Atmosphere and the Ocean, University of Washington, Seattle. WA 98195, USA Present address: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW, UK.
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Abstract

The equation for small-amplitude disturbances to an unbounded flow of constant shear on a beta-plane has well-known solutions of a particularly simple form. In physical terms such solutions represent a flow in which absolute-vorticity contours, initially taking a wavy configuration, are deformed by the basic-state shear. Here it is shown that, at least in cases where the initial disturbance has long wavelength, the vorticity distribution predicted by such solutions eventually becomes barotropically unstable, as the shearing over of material contours leads to local reversals in the cross-stream gradient of absolute vorticity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 175 , February 1987 , pp. 463 - 478
Copyright
© 1987 Cambridge University Press

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