## Abstract

The barotropic instability of finite amplitude waves is suggested as a mechanism for explaining the equilibration of a baroclinic wave growing in a meridionally independent vertical shear flow. A quasigeostrophic two-layer channel model on an *f*-plane is used to give evidence for this hypothesis. Three solutions with different flow symmetries are adopted for the analysis. Numerical simulations reveal that the flow symmetry of the initial small amplitude perturbation can have a large impact on wave structure evolution and energetics. The flow symmetry of the first solution forces the wave to excite symmetric life cycles with baroclinic growth and baroclinic decay. The flow symmetries of the other solutions enable the wave to undergo an asymmetric life cycle with baroclinic growth followed by a barotropic decay that occurs when the fundamental wave has a sufficiently large aspect ratio. Accordingly, a linear-stability analysis of a steady barotropic wave reveals an increasing destabilization with increasing aspect ratio. Further evidence for the relevance of barotropic wave instability is obtained by analyzing the stability of a symmetric life cycle with respect to a symmetry-breaking mode. Near the time of barotropic wave equilibration the results are similar to the barotropic analysis. Furthermore, it is found that the equilibration is caused by a pattern that breaks the flow symmetry and shows a high correlation to the normal mode of the linear instability. These results indicate that the barotropic decay occuring in the asymmetric life cycles is initiated by a finite-amplitude wave instability mechanism.

*Corresponding author address:* Thomas Frisius, Meteorologisches Institut, Universität Hamburg, Bundesstraße 55, D-20146 Hamburg, Germany.

Email: frisius@dkrz.de