Non-axisymmetric instability in thin discs

Details Non-axisymmetric instability in thin discs Non-axisymmetric instability in thin discs

Mar 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985mnras.213p...7g&link_type=abstract

Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 213, March 1, 1985, p. 7P-10P.

Astronomy and Astrophysics

Astrophysics

74

Angular Momentum, Astrophysics, Dynamic Stability, Rotating Fluids, Shear Flow, Gas Density, Kelvin-Helmholtz Instability, Rotating Disks, Vortices, Wentzel-Kramer-Brillouin Method

Scientific paper

Theoretical evidence is presented for the inevitability of the appearance of instability in dynamically rotating thin disks. The disk is treated as a parallel shear flow of a thin, compressible, uniform density gas sheet with a constant velocity gradient. A parabolic-cylinder differential equation is used to express the perturbations, which include corotation and Lindblad resonances. Eigenmodes are found to arise in forbidden regions between the resonant turning points. A maximum growth rate is characterized for the eigenmodes (WKB modes). A reflecting boundary is determined necessary for formation of a self-sustained oscillation, and will appear if the density at the inner or outer edge of the disk cuts off on a scale shorter than the radial eigenmode wavelength.

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