Baroclinic instability of a meridionally varying basic state

Abstract

Several problems are addressed herein. They are loosely connected by the theme of resonant triad interactions. The main topic is the finite amplitude evolution of weakly unstable, linear eigenmodes in a meridionally varying version of Phillips' two-layer model. It is shown in chapter four that interactions between neutral modes and the unstable mode strongly influence the evolution of the latter and are capable of stabilising it before significant changes occur in the zonally averaged flow. The evolution of the unstable wave in the absence of such resonant triad effects is also considered and it is shown by example that the combined influence of changes to the mean flow and higher harmonics of the unstable wave is sufficient to equilibrate the unstable wave. (The higher harmonics are unimportant in the meridionally uniform version of this model). The enhanced importance of neutral sidebands and the details of the evolution are interpreted as being consequences of the structure of the eigenmodes of the linear problem. It is shown in chapter three that, near minimum critical shear, meridional variation of the potential vorticity gradient of the basic flow can introduce dramatic changes in the structure of the normal modes. Some aspects of resonant triad dynamics in a meridionally uniform, vertically sheared, two-layer model are considered in chapter two. It is shown that non-linear interactions between a resonant triplet of neutral waves can lead to baroclinic instability. It is also demonstrated that resonant interactions between a slightly supercritical unstable linear mode and two neutral waves can destabilise the weakly finite amplitude equilibration of the unstable mode that would occur in the absence of the sidebands. This demonstration is limited to the case in which the basic state is not close to minimum critical shear. Finally, the work of Loesch (1974) , who examined the evolution of a weakly unstable mode and a pair of neutral waves in a basic flow that is close to minimum critical shear, is repeated with the difference that critical layer effects are included.