The structure and stability of vortices in astrophysical discs
This thesis finds that vortex instabilities are not necessarily a barrier to their potential as sites for planetesimal formation. It is challenging to build planetesimals from dust within the lifetime of a protoplanetary disc and before such bodies spiral into the central star. Collecting matter in vortices is a promising mechanism for planetesimal growth, but little is known about their stability under these conditions. We therefore aim to produce a more complete understanding of the stability of these objects. Previous work primarily focusses on 2D vortices with elliptical streamlines, which we generalise. We investigate how non–constant vorticity and density power law profiles affect stability by applying linear perturbations to equilibrium solutions. We find that non–elliptical streamlines are associated with a shearing flow inside the vortex. A ‘saddle point instability’ is seen for elliptical–streamline vortices with small aspect ratios and we also find that this is true in general. However, only higher aspect ratio vortices act as dust traps. For constant–density vortices with a concentrated vorticity source we find parametric instability bands at these aspect ratios. Models with a density excess show many narrow bands, though with less strongly growing modes than the constant–density solutions. This implies that dust particles attracted to a vortex core may well encounter parametric instabilities, but this does not necessarily prevent dust–trapping. We also study the stability and lifetime of vortex models with a 2D flow in three dimensions. Producing nearly–incompressible 3D models of columnar vortices, we find that weaker vortices persist for longer times in both stratified and unstratified shearing boxes, and stratification is destabilising. The long survival time for weak, elongated vortices makes it easier for processes to create and maintain the vortex. This means that vortices with a large enough aspect ratio have a good chance of surviving and trapping dust for sufficient time in order to build planetesimals.