Finite-Amplitude Stability of Rossby Wave Flow

Abstract

Finite-amplitude stability characteristics of Rossby wave flow are investigated in the context of the inviscid barotropic model on a beta plane. It is shown that a superimposed disturbance, unstable in the linear sense, grows as long as it lags the basic Rossby wave. However, when the disturbance becomes sufficiently large, it alters the phase and the amplitude of the Rossby wave flow. The phase correction of the Rossby wave is to the west and, in time, large enough to reverse the phase relation between the disturbance and the basic wave. At the time when the two become in phase, the growth of the disturbance is halted and subsequently, when the disturbance leads the Rossby wave, the disturbance slowly decays out. The basic Rossby wave equilibrates with a phase and amplitude which differ from their initial values.