The stability of quasi-geostrophic fields induced by potential vorticity sources

A determination of the conditions leading to instabilities which grow in place in quasi-geostrophic fields induced by localized potential vorticity sources is presented. The analysis considers a quasi-geostrophic barotropic flow in a horizontally open domain, and a nondimensional quasi-geostrophic vorticity equation is defined which governs the deviation stream function. Weak forcing is considered, and it is shown that the field induced by the topography is stable while the field induced by the potential vorticity source can be unstable. The growth rate is exponential and a function of nonlinearity and friction, which, if absent, indicates an unstable flowfield. The instability is shown to be capable of changing the flowfield from one quasi-steady state to another, with energy extraction occurring at the source