Finite-Amplitude Baroclinic Waves in a Continuous Model of the Atmosphere

Abstract

The finite-amplitude dynamics of a weakly unstable baroclinic disturbance in an atmosphere with continuous shear and static stability is investigated. The effects of ? (the planetary vorticity gradient), Ekman dissipation and thermal damping are included. The multi-scale analysis demonstrates the existence of two-dynamical regimes. First, under the influence of Ekman friction quasi-steady states are achieved after an oscillatory approach to the equilibrium state. It is shown that under the influence of friction long zonal waves possess a weak instability. Second, under the joint influence of Ekman friction and thermal damping (of the simplest Newtonian cooling model) a true asymptotic state is achieved. The amplitude is calculated and is shown to be independent of the thermal damping ? when ? is small. The rectified beat flux is calculated in the steady finite amplitude state. It is proportional to ?. The beat flux is proportional to the difference between the basic temperature gradient and a critical value which increases with both ? and N, the Brunt-Väisälä frequency.