Exploration of perturbations of accretion disks

This thesis investigates the hydrodynamic structure and stability of accretion disks, with particular emphasis on the role of viscosity and its effect on small perturbations. Starting from the fundamental fluid equations—continuity and momentum conservation—the steady-state solutions for a geometrically thin, axisymmetric disk in hydrostatic equilibrium are derived. The viscous stress tensor is introduced to describe the transport of angular momentum due to internal friction within the disk. Perturbations are then applied to the disk leading to a coupled system of equations that relate density and velocity perturbations. Assuming wave-like solutions, dispersion relations are obtained for both inviscid and viscous cases. The results demonstrate that the inclusion of viscosity introduces a dissipative term, yet the disks remain stable, consistent with the properties of the unperturbed steady-state model.