As wind energy technology continues to take the helm of renewable energy deployed throughout the world, and wind farms become a more common sight on the horizon, increased emphasis is placed on wind farm aerodynamics. Obtaining insight into this complex flow problem requires a deeper understanding of the nature of individual wind turbine wakes, and subsequently wake interactions. The topic of wake stability and wake meandering, has received particular attention in recent years. Recent work by Larsen et al. [1] investigated this wake meandering phenomenon based on the hypothesis that the wake behaves as a passive tracer, governed by large-scale lateral and horizontal turbulent components. In contrast, Medici and Alfredsson [2] propose that a meandering mechanism similar to bluff body vortex shedding is responsible for the wake oscillations of their two-bladed model. Thus conflicting views with respect to the triggering mechanisms of wake instability exist and are addressed in this thesis. The approach taken was to use a simple inviscid vortex ring (VR) modelling method to represent the developing rotor wake. This allows for a straight forward investigation and comparison of the impact of uniform, yawed and sheared flow conditions on the development of the wake, with the additional possibility of including ground effect. The phenomenon of vortex filament interaction or leapfrogging, could play a role in the observation of unsteady phenomena and is therefore also addressed. Such a study is hence performed in light of recent conflicting views on the causes of wake meandering. The main conclusion from this study is that the presence of the ground and external perturbations, most notably changes in the wake pitch and the rotor thrust coefficient, can significantly affect the steady development of the wake. The phenomenon of vortex filament leapfrogging, whilst displaying interesting periodic behaviour, does not correlate with periodic wake behaviour reported in Medici et al. [2]. However, in the absence of unsteady inflow, it is shown that the wake of a Horizontal Axis Wind Turbine (HAWT) is certainly prone to displaying unstable, dynamic behaviour caused by these additional factors.