This thesis presents an investigation into the dynamics of vortex rings impacting a sharply-stratified density interface. This problem has a long history and is important for understanding how individual eddies in stratified ...

This thesis examines previously unresolved issues regarding the fluid dynamics of the spread of buoyant water into a rotating environment. We focus in particular on the role that finite potential vorticity and background ...

e consider time-dependent solutions of the Einstein-Maxwell equations using anti–de Sitter (AdS) boundary conditions, and provide the first counterexample to the weak cosmic censorship conjecture in four spacetime dimensions. ...

Numerical relativity has proven to be a successful and robust tool for non-perturbative studies of gravitational phenomena in the highly dynamical and/or non-linear regime. Perhaps the most prominent achievement in the ...

The age of gravitational-wave astronomy has begun. Gravitational waves are propagating spacetime perturbations ($\textit{“ripples in the fabric of space-time”}$) predicted by Einstein’s theory of General Relativity. These ...

In this thesis, three problems motivated by the possibility of use of phase change materials in buildings are presented. First, a model for the response of phase change material (PCM) to a varying room temperature is ...

The overall aim of this thesis is to gain a better understanding of certain key attributes and processes in the Upper Troposphere/Lower Stratosphere (UTLS). This work involves exploring the interactions between radiation ...

This thesis considers the numerical solution to elliptic boundary value problems (BVPs) in convex domains. Specifically we look at the two-dimensional problem in a polygon, and the three dimensional problem in a polyhedron. ...

In this thesis I investigate a number of problems in the nonlinear stability of density stratified plane Couette flow. I begin by describing the history of transient growth phenomena, and in particular the recent application ...