Séminaire
We undertake a detailed analysis of linear stability of the 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 advance analytically in the limit of long-wave disturbances and small-amplitude topography, and use direct collocation method in general case. Different kinds of instabilities due to resonances of frontal, Rossby and topographic waves are identified and quantified. A swap in the leading long-wave instability from the classical barotropic one, resulting from the resonance of two frontal waves, to the baroclinic one, 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 inter-compared with the help of a new-generation well-balanced finite-volume code for multi-layer rotating shallow water equations. The results of the saturation for different instabilities are shown to be very different, producing different secondary coherent structures. The influence of the topography on these processes is highlighted.