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In chapter 1, some fundamental concepts about inertial instability in a general geophysical context are reviewed. The instability is described as a parcel instability, and an axisymmetric linear stability analysis is presented. The general form of the dispersion relation is discussed, and the linear instability problem is described in terms of a variational principle. In chapter 2, the special case of linear equatorial inertial instability is studied. Conditions leading to instability in the equatorial stratosphere and mesosphere are described, and some of the existing linear stability theory is reviewed. For the axisymmetric case, the theory is extended to demonstrate the scaling for the most unstable vertical wavenumber. The inability of the simple linear theory to satisfactorily explain the observations is discussed. In chapter 3, the linear instability of a more complicated equatorial flow with a 'slow' vertical variation is considered. The analysis uses a JWKB method, the results of which are compared with numerical simulations of the problem. The vertical variation leads to a reduction in the expected growth rate. There are also variations in the vertical wavenumber, although these do not seem to be sufficient to explain the large vertical scales present in observations. In chapter 4, a theory is presented for the weakly nonlinear evolution of axisymmetric inertial instability. In chapter 5, aspects of more strongly unstable flows are discussed, based on the results of numerical simulations of the axisymmetric instability.

This thesis is concerned with dynamical coupling between the stratosphere and troposphere. The first part of the thesis examines mechanisms whereby dynamical perturbations to the upper stratosphere can lead to a significant response in the lower stratosphere, looking particularly at how this response is determined by the extra-tropical dynamics. A one dimensional model is used to show that the response is much greater when the external parameters are such that the flow has multiple stable states. The same principle is shown to apply to a fully three dimensional flow and does not depend qualitatively on the representation of the troposphere and tropospheric wave forcing. The dependence of the response on the height of the applied dynamical perturbation, the amplitude of planetary wave forcing, and the relaxation to radiative equilibrium temperatures is considered. In the second part of the thesis we consider the interhemispheric differences in the extratropical seasonal cycle and suggest that resonance of topographically forced waves with free travelling planetary waves could be in part responsible for these differences. The seasonal cycle in mass upwelling in the tropical lower stratosphere is also considered. In particular we look at the differences in this upwelling caused by the strength and location of tropospheric wave driving, the thermal relaxation timescale of the atmosphere, baroclinic instability, and the seasonal cycle in the tropospheric radiative equilibrium temperature field. Finally we consider the interannual variability seen in the tropical mass upwelling. We quantify the different parts of this variability – the part that can be considered forced variability and the part that arises due to internal variability. We suggest that the high forced variability seen in the mass upwelling may be due to it being linked, via extratropical wave driving, to sea surface temperatures.

It is a characteristic of the middle atmosphere that, for the most part, it is strongly stably stratified and rapidly rotating. These two conditions respectively act to inhibit the vertical and latitudinal motion of air. A consequence of this is that the middle atmosphere is particularly amenable to simplifications in terms both of describing it, and of modelling it. It can be treated to a first approximation as axisymmetric, since middle atmospheric conditions often vary much more with latitude and height than with longitude. Although air mass motion in the meridional plane is inhibited in the middle atmosphere, there is good evidence of a persistent mean meridional circulation (MMC) on seasonal timescales. This meridional circulation provides a means by which anthropogenic gases can enter the stratosphere, be carried out to the mesosphere and descend over the poles. Thus, it is of great importance from the viewpoint of photo-chemistry, and the ozone hole. The first part of this dissertation is concerned with the middle atmosphere as simplified by taking the zonal means of the relevant quantities, that is, making it axisymmetric. The climatology of the zonal-mean observed atmosphere is discussed. The main discussion is concerned with the generation of a MMC in such model atmospheres. First an analytic model is discussed, after Eliassen (1951), showing the importance of zonal-mean heating and zonal-mean mechanical forcing in the generation of the MMC. The origin of these forcings in terms of wave-mean interaction is discussed.

This research develops an integrated approach for understanding coastal eutrophication processes. This is based upon numerical modelling of the production of land-based nutrients and their transport to coastal waters, using GIS and remote sensing. This addresses primarily non-point sources (e.g. runoff from agricultural land and soil erosion), but recognises the importance of point sources (e.g. sewerage effluent). Whereas the latter are discharged at identifiable locations with quantified runoff volumes, non-point sources are diffuse and seasonably variable depending on the climate and rainfall. This makes their determination using a modelling approach especially important. The specific focus was the south-east of Malta. The methodology was based upon: 1) a flow routing model, derived from a DEM, to determine the patterns of drainage to the coast; 2) coupling this with the Soil Conservation Service (SCS) model to estimate runoff volumes for given rainfall and classified land use data. 3) an Export Coefficient (EC) Model to estimate nitrate and phosphate loadings; 4) the EROSION 3D model to predict the rate of soil erosion as a potential source of soil-bound phosphorus and contributor to turbidity in coastal waters; 5) inclusion of sewage discharge volumes and nutrient input from coastal point sources; 6) estimation of the spatial distribution of the water mixing time, using Rhodamine dye tracing techniques, in order to quantify dilution; and 7) water quality mapping in coastal waters to assess the effects of nutrient loading upon coastal waters. Corrections for the interfering influences of bottom effects were implemented.