It is shown that a vertical asymmetry in the friction qualitatively influences the equilibration of nonlinear quasi-geostrophic unstable baroclinic waves. Specifically, the sense of this asymmetry is a crucial factor that dictates whether the equilibrated state is generally a steady multiple wave state or a vacillation. The former is generally the preferred form of an equilibrated state for the case of having a larger friction in the lower layer than in the upper layer. In contrast, vacillation is a preferred form for the case of an opposite asymmetry in the friction. The limit cycle has a weaker time mean component. A zonal barotropic jet is additionally induced by the finite amplitude waves.
The degree of irregularity in the vacillation increases with the frictional asymmetry. An equilibrated state of chaos prevails over a wide range of parametric conditions. The corresponding return map suggests that the chaos is not a Lorenzian strange attractor. Its property has been examined in terms of the Lyapunov characteristic number.
The energetics diagnosis confirms that the sense of the asymmetry in the friction controls the sense of the frictionally induced secondary circulation. This underlines the character of the influence of the frictional asymmetry. The findings of this analysis may have a bearing on the effects on the dynamics of a large-scale flow, due to the breaking of subgrid scale gravity waves, found in the recent high resolution, GCM/NWP models.