Strongly Nonlinear Vacillation in Baroclinic Waves

Abstract

The dynamics of vacillation is examined for the case where several waves are unstable and the wave-mean flow interactions are shown to be the same as in the case where only one wave is unstable, as has been done previously. However, the wave-wave interactions are at least as large as any of the other energy conversions. These vacillations occur for parameter settings similar to those of the atmosphere. Two classes of vacillation (wavenumber and structural) exist for different forcings, and these classes are distinguished not by differences in the wave-mean flow dynamics but only by the number of waves interacting effectively with the mean flow. Amplitude vacillation would be a special case of the wavenumber vacillation found here, for weak wave-wave interactions. It is suggested that only structural vacillation is likely to he found in the atmosphere based on the sensitivity of the amplitude and wavenumber vacillations to weak perturbations.