Amplitude Vacillation on an f-Plane

Abstract

Amplitude vacillation is studied using a spectral version of the two-level quasi-geostrophic model in an f-plane channel. The numerical results are compared to those of a weakly nonlinear asymptotic theory of amplitude vacillation formulated by Pedlosky (1970, 1971, 1972). Although the two systems give similar results for weak instabilities, they are quite different for larger instabilities. In particular, the transition from steady to vacillating waves requires much greater instability than it does in the asymptotic theory for moderate dissipation levels. The energetics of the amplitude vacillation cycles are discussed using a nonstandard formulation for the energy, and it is shown that there are significant differences between the energetics for small and large instabilities. Even for large instabilities, however, the amplitude vacillation period is much longer than it appears to be in laboratory experiments or in the atmosphere.