Piecewise-Constant Vortices in a Two-Layer Shallow-Water Flow

Vortices are a main feature of oceanic circulation, and thus have often been studied, mostly with a quasi-geostrophic model: stationary solutions such as tripoles have been found (Carton and Legras, 1994; Corréard and Carton, 1999). Recently, vortex stability has been investigated in a shallow-water framework (Dewar and Killworth, 1995; Carton and Baey, 2000; Stegner and Dritschel, 2000). These studies showed that the potential vorticity profile of the vortex, as well as its size (Burger number, see Benilov et al., 1998) and its intensity (Rossby number) are crucial for its stability. But they defined the vortex via its velocity profile, thus changing potential vorticity with stratification. In the present study, the potential vorticity profile of the vortex is given independently of the other parameters and is reduced to a very simple form: piecewise-constant.