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Centrifugal, barotropic and baroclinic instabilities of isolated ageostrophic anticyclones in the two-layer rotating shallow water model and their nonlinear saturation

Published online by Cambridge University Press:  27 November 2014

Noé Lahaye  and
Vladimir Zeitlin
Noé Lahaye*
Affiliation:
Laboratoire de Météorologie Dynamique, UPMC-ENS, 24 rue Lhomond, 75005 Paris, France
Vladimir Zeitlin
Affiliation:
Laboratoire de Météorologie Dynamique, UPMC-ENS, 24 rue Lhomond, 75005 Paris, France Institut Universitaire de France
*
†Email address for correspondence: lahaye@lmd.ens.fr
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Abstract

Instabilities of isolated anticyclonic vortices in the two-layer rotating shallow water model are studied at Rossby numbers up to two, with the main goal to understand the interplay between the classical centrifugal instability and other ageostrophic instabilities. We find that different types of instabilities with low azimuthal wavenumbers exist, and may compete. In a wide range of parameters, an asymmetric version of the standard centrifugal instability has larger growth rate than the latter. The dependence of the instabilities on the parameters of the flow, i.e. Rossby and Burger numbers, vertical shear and the ratios of the layers’ thicknesses and densities, is investigated. The zones of dominance of each instability are determined in the parameter space. Nonlinear saturation of these instabilities is then studied with the help of a high-resolution finite-volume numerical scheme, by using the unstable modes identified from the linear stability analysis as initial conditions. Differences in nonlinear development of the competing centrifugal and ageostrophic barotropic instabilities are evidenced. A nonlinear mechanism of axial symmetry breaking during the saturation of the centrifugal instability is displayed.

JFM classification

Instability: Instability Geophysical and Geological Flows: Ocean processes Geophysical and Geological Flows: Shallow water flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 762 , 10 January 2015 , pp. 5 - 34
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Copyright
© 2014 Cambridge University Press 

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