Stability of jet flows in a rotating shallow water layer

Resumo

The problem of the stability of an isolated jet flow and two counter-streaming jet flows in a rotating shallow-water layer is considered. These flows are described by exact solutions of the Charny–Obukhov equation with one or two discontinuities of the potential vorticity, respectively. The isolated jet flow is shown to be stable. For the system consisting of two jet flows the dependence of the characteristics of the unstable wave modes on a geometric parameter, namely, the ratio of the spacing between the jet axes to the deformation radius, is determined. On the basis of the contour dynamics method a weakly-nonlinear model of the longwave instability is developed.