The stability of a differentially rotating cylinder of an incompressible perfect fluid

• Published in: Monthly notices of the Royal Astronomical Society Vol. 234; no. 1; pp. 107 - 114
• Main Authors: Sekiya, Minoru, Miyama, Shoken M.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Oxford University Press 01-09-1988
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1093/mnras/234.1.107

The stability criterion for differentially rotating fluid cylinders given by Goldreich, Goodman & Narayan is re-examined. A rotation law of the form $\Omega_0\propto r^{-q}$ is assumed for the unperturbed state, where Ω0, r and q are the angular velocity, the distance from the central star and a constant, respectively. We find that, even for$q\gt\sqrt 3$ a cylinder of an incompressible fluid is unstable provided that the half thickness of the cylinder, a is finite. The growth rate of a small perturbation is proportional to a2 as long as a≪3−q2.