Dynamics of perturbation modes in protoplanetary discs : new effects of self-gravity and velocity shear

Protoplanetary discs, composed of gas and dust, usually surround young stellar objects and serve two main purposes: they determine the accretion of matter onto the central object and also represent sites of planet formation. The accretion proceeds through the transport of angular momentum outwards allowing the disc matter to fall towards the centre. A mechanism responsible for the transport can be turbulence, waves or other coherent structures originating from various instabilities in discs that could, in addition, play a role in the planet formation process. For an understanding of these instabilities, it is necessary to study perturbation dynamics in differentially rotating, or sheared media. Thus, this thesis focuses on new aspects in the perturbation dynamics in non-magnetised protoplanetary discs that arise due to their self-gravity and velocity shear associated with the disc’s differential rotation. The analysis is carried out in the framework of the widely employed local shearing box approximation. We start with 2D discs and then move on to 3D ones. In 2D discs, there are two basic perturbation types/modes – spiral density waves and vortices – that are responsible for angular momentum transport and that can also contribute to accelerating planet formation. First, in the linear regime, we demonstrate that the vortical mode undergoes large growth due to self-gravity and in this process generates density waves via shear-induced linear mode coupling phenomenon. This is noteworthy, because commonly only density waves are considered in self-gravitating discs. Then we investigate vortex dynamics in the non-linear regime under the influence of self-gravity by means of numerical simulations. It is shown that vortices are no longer well-organised and long-lived structures, unlike those occurring in non-self-gravitating discs. They undergo recurring phases (lasting for a few disc rotation periods) of formation, growth and eventual destruction. We also discuss the dust trapping capability of such transient vortices. Perturbation dynamics in 3D vertically stratified discs is richer, as there are more mode types. We first consider non-axisymmetric modes in non-self-gravitating discs and then only axisymmetric modes in the more complicated case when self-gravity is present. Specifically, in non-self-gravitating discs with superadiabatic vertical stratification, motivated by the recent results on the transport properties of incompressible convection, we show that when compressibility is taken into account, the non-axisymmetric convective mode excites density waves via the same shear-induced linear mode coupling mechanism mentioned above. These generated density waves transport angular momentum outwards in the trailing phase, and we suggest that they may aid and enhance the transport due solely to convection in the non-linear regime, where the latter becomes outward. In the final part of the thesis, we carry out a linear analysis of axisymmetric vertical normal modes in stratified self-gravitating discs. Although axisymmetric modes do not display shear-induced couplings, their analysis provides insight into how gravitational instabilities develop in the 3D case and their onset criterion. We examine how the structure of dispersion curves and eigenfunctions of 3D modes are influenced by self-gravity, which mode first becomes gravitationally unstable and thus determines the onset criterion and nature of the gravitational instability in stratified discs. We also contrast the more exact instability criterion obtained with our 3D model with that of density waves in 2D discs. Based on these findings, we discuss the origin of 3D behaviour of perturbations involving noticeable disc surface distortions, as seen in some numerical simulations of self-gravitating discs.