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Instabilities of two-layer shallow-water flows with vertical shear in the rotating annulus

Published online by Cambridge University Press:  18 September 2009

J. GULA ,
V. ZEITLIN  and
R. PLOUGONVEN
J. GULA
Affiliation:
Laboratoire de Météorologie Dynamique, ENS and University P. and M. Curie, 24, rue Lhomond 75005, Paris, France
V. ZEITLIN*
Affiliation:
Laboratoire de Météorologie Dynamique, ENS and University P. and M. Curie, 24, rue Lhomond 75005, Paris, France
R. PLOUGONVEN
Affiliation:
Laboratoire de Météorologie Dynamique, ENS and University P. and M. Curie, 24, rue Lhomond 75005, Paris, France
*
†Email address for correspondence: zeitlin@lmd.ens.fr
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Abstract

Being motivated by the recent experiments on instabilities of the two-layer flows in the rotating annulus with super-rotating top, we perform a full stability analysis for such system in the shallow-water approximation. We use the collocation method which is benchmarked by comparison with analytically solvable one-layer shallow-water equations linearized about a state of cyclogeostrophic equilibrium. We describe different kinds of instabilities of the cyclogeostrophically balanced state of solid-body rotation of each layer (baroclinic, Rossby–Kelvin (RK) and Kelvin–Helmholtz (KH) instabilities), and give the corresponding growth rates and the structure of the unstable modes. We obtain the full stability diagram in the space of parameters of the problem and demonstrate the existence of crossover regions where baroclinic and RK, and RK and KH instabilities, respectively, compete having similar growth rates.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 638 , 10 November 2009 , pp. 27 - 47
Copyright
Copyright © Cambridge University Press 2009

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