Dynamical instabilities in disc-planet interactions
Protoplanetary discs can be dynamically unstable due to structure induced by an embedded giant planet. In this thesis, I discuss the stability of such systems and explore the consequence of instability on planetary migration. I present semi-analytical models to understand the formation of the unstable structure induced by a Saturn mass planet, which leads to vortex formation. I then investigate the effect of such vortices on the migration of a Saturnmass planet using hydrodynamic simulations. I explain the resulting nonmonotonic behaviour in the framework of type III planetary migration. I then examine the role of disc self-gravity on the vortex instabilities. It can be shown that self-gravity has a stabilising effect. Linear numerical calculations confirms this. When applied to disc-planet systems, modes with small azimuthal wavelengths are preferred with increasing disc selfgravity. This is in agreement the observation that more vortices develop in simulations with increasing disc mass. Vortices in more massive discs also resist merging. I show that this is because inclusion of self-gravity sets a minimal vortex separation preventing their coalescence, which would readily occur without self-gravity. I show that in sufficiently massive discs vortex modes are suppressed. Instead, global spiral instabilities develop. They are interpreted as disturbances associated with the planet-induced structure, which interacts with the wider disc leading to instability. I carry out linear calculations to confirm this physical picture. Results from nonlinear hydrodynamic simulations are also in agreement with linear theory. I give examples of the effect of these global modes on planetary migration, which can be outwards, contrasting to standard inwards migration in more typical disc models. I also present the first three-dimensional computer simulations examining planetary gap stability. I confirm that the results discussed above, obtained from two-dimensional disc approximations, persist in three-dimensional discs.