Forced disturbances in a zero absolute vorticity gradient environment

Observations show the presence of localized regions in the atmosphere with diminished potential vorticity gradients, an example being the tropical upp er troposphere where convective heating plays an important role. The presen t work investigates the effect of forcing on the evolution of Rossby waves in a zero potential vorticity gradient environment. As a preliminary invest igation, the barotropic case is studied, where the analog of potential vort icity is absolute vorticity. A forcing term is employed to model thermal fo rcing in the real atmosphere. The analytic solution of the linearized problem shows that the streamfuncti on grows in time and eventually develops a nonlinear critical layer. The pr esence of forcing within the critical layer is found to drive the dynamics. The numerical solution of the nonlinear problem within the critical layer shows that the nonlinearity and the forcing act together to halt the growth as coherent vortices develop in a nonlinear oscillatory regime. At long ti mes, the critical layer solution settles down to a quasi steady state consi sting of relatively large amplitude stationary vortices with a set of small amplitude steadily propagating vortices superimposed. These results are co ntrasted with the results of previous unforced problems.