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

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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, Poincar 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.

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关键词：

Theoretical or Mathematical/ finite volume methods flow instability Rossby waves rotational flow shallow water equations/ coupled density fronts two-layer rotating shallow-water model geostrophically balanced double density fronts pseudospectral collocation method phase locking frontal waves Rossby waves topographic waves Poincare waves long-wave instability classical barotropic form baroclinic form new-generation well-balanced finite-volume code multilayer rotating shallow-water equations secondary coherent structures/ A4720 Hydrodynamic stability and instability A4730 Rotational flow, vortices, buoyancy and other flows involving body forces A4735 Waves in fluid dynamics A0260 Numerical approximation and analysis A4710 General fluid dynamics theory, simulation and other computational methods