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.
