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The stability of quasi-geostrophic fields induced by potential vorticity sources

Published online by Cambridge University Press:  20 April 2006

Lee-Or Merkine
Lee-Or Merkine
Affiliation:
Department of Mathematics, Technion-Israel Institute of Technology, Haifa
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Abstract

The stability of quasi-geostrophic barotropic fields induced by localized finite-amplitude potential vorticity sources or topographies which depend only on the zonal direction is investigated both analytically and numerically. The analytical study is for weak forcing. It demonstrates that the field induced by the topography is stable whereas the field induced by the potential vorticity source can be unstable. The growth rate is exponential and is a function of both nonlinearity and friction. In the absence of friction the flow field is always unstable. The instability takes the form of a current whose meridional wavenumber is that of a stationary Rossby wave. In the zonal direction the current exhibits long-scale oscillations and exponential decay. The numerical computations which are for strong forcing verify all the indications of the asymptotic study. They show a rapid exponential growth of a non-propagating but oscillatory wave packet whose location is fixed relative to the forcing. The zonal scale of the packet is that of a stationary Rossby wave. For weak forcing the instability can be responsible for changing the flow field from one quasi-steady state to another where the energy extraction takes place in the region of the source. It is efficient for potential vorticity sources whose length scale is comparable to the length scale of stationary Rossby waves. In agreement with the asymptotic study, fields induced by strong topographic forcing are found to be stable. The asymptotic analysis is also applied to baroclinic flows where the investigation is performed in the framework of the two-layer model. It is demonstrated that the same mechanism which operates in barotropic systems can also destabilize baroclinic flows which possess subcritical shears.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 116 , March 1982 , pp. 315 - 342
Copyright
© 1982 Cambridge University Press

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