The dynamics of the atmosphere and ocean are dominated by slowly evolving, large-scale motions. However, fast, small-scale motions in the form of inertia-gravity waves are ubiquitous. These waves are of great importance for the circulation of the atmosphere and oceans, mainly because of the momentum and energy they transport and because of the mixing they create upon breaking. So far the study of inertia-gravity waves has answered a number of questions about their propagation and dissipation, but many aspects of their generation remain poorly understood. The interactions that take place between the slow motion, termed balanced or vortical motion, and the fast inertia-gravity wave modes provide mechanisms for inertia-gravity wave generation. One of these is the instability of balanced flows to gravity-wave-like perturbations; another is the so-called spontaneous generation in which a slowly evolving solution has a small gravity-wave component intrinsically coupled to it. In this thesis, we derive and study a simple model of inertia-gravity wave generation which considers the evolution of a small-scale, small amplitude perturbation superimposed on a large-scale, possibly time-dependent °ow. The assumed spatial-scale separation makes it possible to apply a WKB approach which models the perturbation to the flow as a wavepacket. The evolution of this wavepacket is governed by a set of ordinary differential equations for its position, wavevector and its three amplitudes. In the case of a uniform flow (and only in this case) the three amplitudes can be identifed with the amplitudes of the vortical mode and the two inertia-gravity wave modes. The approach makes no assumption on the Rossby number, which measures the time-scale separation between the balanced motion and the inertia-gravity waves. The model that we derive is first used to examine simple time-independent flows, then flows that are generated by point vortices, including a point-vortex dipole and more complicated flows generated by several point vortices. Particular attention is also paid to a flow with uniform vorticity and elliptical streamlines which is the standard model of elliptic instability. In this case, the amplitude of the perturbation obeys a Hill equation. We solve the corresponding Floquet problem asymptotically in the limit of small Rossby number and conclude that the inertia-gravity wave perturbation grows with a growth rate that is exponentially small in the Rossby number. Finally, we apply the WKB approach to a flow obtained in a baroclinic lifecycle simulation. The analysis highlights the importance of the Lagrangian time dependence for inertia-gravity wave generation: rapid changes in the strain field experienced along wavepacket trajectories (which coincide with fluid-particle trajectories in our model) are shown to lead to substantial wave generation.

In this study we investigate the interactions between two co-rotating vortices. These vortices are subject to rapid rotation and stable stratification such as are found in planetary atmospheres and oceans. By conducting a large number of simulations of vortex interactions, we intend to provide an overview of the interactions that could occur in geophysical turbulence. We consider a wide parameter space covering the vortices height-to-width aspect-ratios, their volume ratios and the vertical offset between them. The vortices are initially separated in the horizontal so that they reside at an estimated margin of stability. The vortices are then allowed to evolve for a period of approximately 20 vortex revolutions. We find that the most commonly observed interaction under the quasi-geostrophic (QG) regime is partial-merger, where only part of the smaller vortex is incorporated into the larger, stronger vortex. On the other hand, a large number of filamentary and small scale structures are generated during the interaction. We find that, despite the proliferation of small-scale structures, the self-induced vortex energy exhibits a mean `inverse-cascade' to larger scale structures. Interestingly we observe a range of intermediate-scale structures that are preferentially sheared out during the interactions, leaving two vortex populations, one of large-scale vortices and one of small-scale vortices. We take a subset of the parameter space used for the QG study and perform simulations using a non-hydrostatic model. This system, free of the layer-wise two-dimensional constraints and geostrophic balance of the QG model, allows for the generation of inertia-gravity waves and ageostrophic advection. The study of the interactions between two co-rotating, non-hydrostatic vortices is performed over four different Rossby numbers, two positive and two negative, allowing for the comparison of cyclonic and anti-cyclonic interactions. It is found that a greater amount of wave-like activity is generated during the interactions in anticyclonic situations. We also see distinct qualitative differences between the interactions for cyclonic and anti-cyclonic regimes.