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Instabilities of coupled density fronts and their nonlinear evolution in the two-layer rotating shallow-water model: influence of the lower layer and of the topography

Published online by Cambridge University Press:  25 January 2013

Bruno Ribstein  and
Vladimir Zeitlin
Bruno Ribstein*
Affiliation:
LMD, Université Pierre et Marie Curie, and ENS, 24 rue Lhomond, 75005 Paris, France
Vladimir Zeitlin
Affiliation:
LMD, Université Pierre et Marie Curie, and ENS, 24 rue Lhomond, 75005 Paris, France Institut Universitaire de France, 75005 Paris, France
*
†Email address for correspondence: ribstein@lmd.ens.fr
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Abstract

We undertake a detailed analysis of linear stability of geostrophically balanced double density fronts in the framework of the two-layer rotating shallow-water model on the $f$-plane with topography, the latter being represented by an escarpment beneath the fronts. We use the pseudospectral collocation method to identify and quantify different kinds of instabilities resulting from phase locking and resonances of frontal, Rossby, Poincaré and topographic waves. A swap in the leading long-wave instability from the classical barotropic form, resulting from the resonance of two frontal waves, to a baroclinic form, resulting from the resonance of Rossby and frontal waves, takes place with decreasing depth of the lower layer. Nonlinear development and saturation of these instabilities, and of an instability of topographic origin, resulting from the resonance of frontal and topographic waves, are studied and compared with the help of a new-generation well-balanced finite-volume code for multilayer rotating shallow-water equations. The results of the saturation for different instabilities are shown to produce very different secondary coherent structures. The influence of the topography on these processes is highlighted.

JFM classification

Geophysical and Geological Flows: Gravity currents Instability: Instability Geophysical and Geological Flows: Rotating flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 716 , 10 February 2013 , pp. 528 - 565
Copyright
©2013 Cambridge University Press

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