The dynamical stability of differentially rotating discs with constant specific angular momentum
Abstract
The dynamical stability of a differentially rotating disc (or torus) of fluid of uniform entropy and uniform specific angular momentum is investigated. Such a fluid is neutrally stable to axisymmetric perturbations. Nonaxisymmetric perturbations are considered as part of a global stability analysis. A general study of the normal mode eigenvalue problem and the explicit analytic solution of a pair of particular limiting cases are presented. The fastest growing eigenmodes by numerical integration of the full linearized equations for more general cases are derived. The overall result is that the tori are unstable to low order nonaxisymmetric modes and that the modes grow on a dynamical timescale. Because of the strength of the instability, similar unstable modes must exist in tori of nonuniform entropy or of nonuniform specific angular momentum.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 June 1984
 DOI:
 10.1093/mnras/208.4.721
 Bibcode:
 1984MNRAS.208..721P
 Keywords:

 Accretion Disks;
 Angular Momentum;
 Astronomical Models;
 Dynamic Stability;
 Rotating Fluids;
 Toruses;
 Eigenvalues;
 Perturbation Theory;
 Polytropic Processes;
 Quasars;
 Astrophysics