Nonlinear Evolution of Forced Rossby Waves in a Baro tropic Atmosphere Part I: Stability Properties of Forced Rossby Waves

Abstract

A barotropic quasi-geostrophic inviscid β-plane channel model with simple surface topography is constructed to investigate the nonlinear temporal behavior of forced Rossby waves. In particular, an emphasis is placed on the consequent evolution of forced Rossby waves due to growing unstable perturbations, in connection with the wave amplification observed during the blocking and the sudden warming.
This paper consists of two parts: In Part I, we investigate linear stability properties of forced Rossby waves. The presence of surface topography is found to have a significant effect to destabilize the basic flow. When the forced Rossby wave has the largest horizontal scale, the flow becomes unstable and produces two kinds of instabilities: One is the topographic instability for the superresonant flow and the other is for the subresonant flow. The former, which can be represented in a loworder model of Charney and DeVore (1979), produces a standing type perturbation characterized by the form-drag through topography, while the latter, which cannot be represented in the low-order model, is characterized by the interaction between wave components of the perturbation and the basic forced Rossby wave. With the decrease of the zonal flow speed, the horizontal scale of the perturbation becomes smaller, as is expected from the necessary condition for instability.
It is also found that the topographic instability does not appear when the meridional wavenumber of the forced Rossby wave is even.