Abstract
Observations show the presence of localized regions in the atmosphere with diminished potential vorticity gradients, an example being the tropical upper troposphere where convective heating plays an important role. The present work investigates the effect of forcing on the evolution of Rossby waves in a zero potential vorticity gradient environment. As a preliminary investigation, the barotropic case is studied, where the analog of potential vorticity is absolute vorticity. A forcing term is employed to model thermal forcing in the real atmosphere.
The analytic solution of the linearized problem shows that the streamfunction grows in time and eventually develops a nonlinear critical layer. The presence 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 times, the critical layer solution settles down to a quasi steady state consisting of relatively large amplitude stationary vortices with a set of small amplitude steadily propagating vortices superimposed. These results are contrasted with the results of previous unforced problems.
Corresponding author address: Mr. Paul F. Choboter, Department of Mathematical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada.
Email: choboter@math.ualberta.ca