Free Rossby Wave Instability at Finite Amplitude

Abstract

The finite-amplitude evolution of the instability of a nonparallel basic-state flow and the basic state are studied. The basic state consists of a free Rossby wave in an inviscid, barotropic beta-plane model. The method of multiple time scales is used to obtain the weakly nonlinear evolution of the system on the long time scale corresponding to the slow growth of the slightly unstable perturbation. The results of the analysis show that, as the perturbation grows, both the amplitude and phase of the Rossby wave are modified, producing a nonlinear feedback which acts to stabilize the perturbation. Feedback due to nonlinearly produced harmonics can be either stabilizing or destabilizing to the perturbation. The total feedback is usually stabilizing and leads to an oscillatory exchange between the Rossby wave and perturbation. The mechanism responsible for the nonlinear feedback is the tilted trough mechanism.